diff --git a/spec/core/integration/AsymmetricEqualityTestersSpec.js b/spec/core/integration/AsymmetricEqualityTestersSpec.js
new file mode 100644
index 00000000..1ccf2801
--- /dev/null
+++ b/spec/core/integration/AsymmetricEqualityTestersSpec.js
@@ -0,0 +1,222 @@
+describe('Asymmetric equality testers (Integration)', function () {
+  function verifyPasses(expectations, setup) {
+    it('passes', function (done) {
+      var env = new jasmineUnderTest.Env();
+      env.it('a spec', function () {
+        expectations(env);
+      });
+
+      var specExpectations = function (result) {
+        expect(result.status).toEqual('passed');
+        expect(result.passedExpectations.length)
+          .withContext('Number of passed expectations')
+          .toEqual(1);
+        expect(result.failedExpectations.length)
+          .withContext('Number of failed expectations')
+          .toEqual(0);
+        expect(result.failedExpectations[0] && result.failedExpectations[0].message)
+          .withContext('Failure message')
+          .toBeUndefined();
+      };
+
+      env.addReporter({specDone: specExpectations, jasmineDone: done});
+      env.execute();
+    });
+  }
+
+  function verifyFails(expectations) {
+    it('fails', function (done) {
+      var env = new jasmineUnderTest.Env();
+      env.it('a spec', function () {
+        expectations(env);
+      });
+
+      var specExpectations = function (result) {
+        expect(result.status).toEqual('failed');
+        expect(result.failedExpectations.length)
+          .withContext('Number of failed expectations')
+          .toEqual(1);
+        expect(result.failedExpectations[0].message)
+          .withContext('Failed with a thrown error rather than a matcher failure')
+          .not.toMatch(/^Error: /);
+        expect(result.failedExpectations[0].matcherName).withContext('Matcher name')
+          .not.toEqual('');
+      };
+
+      env.addReporter({specDone: specExpectations, jasmineDone: done});
+      env.execute();
+    });
+  }
+
+  describe('any', function () {
+    verifyPasses(function (env) {
+      env.expect(5).toEqual(jasmineUnderTest.any(Number));
+    });
+
+    verifyFails(function (env) {
+      env.expect("five").toEqual(jasmineUnderTest.any(Number));
+    });
+  });
+
+  describe('anything', function () {
+    verifyPasses(function (env) {
+      env.expect('').toEqual(jasmineUnderTest.anything());
+    });
+
+    verifyFails(function (env) {
+      env.expect(null).toEqual(jasmineUnderTest.anything());
+    });
+  });
+
+  describe('arrayContaining', function () {
+    verifyPasses(function (env) {
+      env.addCustomEqualityTester(function (a, b) {
+        return a.toString() === b.toString();
+      });
+      env.expect([1, 2, 3]).toEqual(jasmineUnderTest.arrayContaining(["2"]));
+    });
+
+    verifyFails(function (env) {
+      env.expect(null).toEqual(jasmineUnderTest.arrayContaining([2]));
+    });
+  });
+
+  describe('arrayWithExactContents', function () {
+    verifyPasses(function (env) {
+      env.addCustomEqualityTester(function (a, b) {
+        return a.toString() === b.toString();
+      });
+      env.expect([1, 2]).toEqual(jasmineUnderTest.arrayWithExactContents(["2", "1"]));
+    });
+
+    verifyFails(function (env) {
+      env.expect([]).toEqual(jasmineUnderTest.arrayWithExactContents([2]));
+    });
+  });
+
+  describe('empty', function () {
+    verifyPasses(function (env) {
+      env.expect([]).toEqual(jasmineUnderTest.empty());
+    });
+
+    verifyFails(function (env) {
+      env.expect([1]).toEqual(jasmineUnderTest.empty());
+    });
+  });
+
+  describe('falsy', function () {
+    verifyPasses(function (env) {
+      env.expect(false).toEqual(jasmineUnderTest.falsy());
+    });
+
+    verifyFails(function (env) {
+      env.expect(true).toEqual(jasmineUnderTest.falsy());
+    });
+  });
+
+  describe('mapContaining', function () {
+    if (jasmine.getEnv().hasFunctioningMaps()) {
+      verifyPasses(function (env) {
+        var actual = new Map();
+        actual.set('a', "2");
+        var expected = new Map();
+        expected.set('a', 2);
+
+        env.addCustomEqualityTester(function (a, b) {
+          return a.toString() === b.toString();
+        });
+
+        env.expect(actual).toEqual(jasmineUnderTest.mapContaining(expected));
+      });
+    } else {
+      it('passes', function() {
+        jasmine.getEnv().pending('Browser has incomplete or missing support for Maps');
+      });
+    }
+
+    if (jasmine.getEnv().hasFunctioningMaps()) {
+      verifyFails(function (env) {
+        env.expect('something').toEqual(jasmineUnderTest.mapContaining(new Map()));
+      });
+    } else {
+      it('fails', function() {
+        jasmine.getEnv().pending('Browser has incomplete or missing support for Maps');
+      });
+    }
+  });
+
+  describe('notEmpty', function () {
+    verifyPasses(function (env) {
+      env.expect([1]).toEqual(jasmineUnderTest.notEmpty());
+    });
+
+    verifyFails(function (env) {
+      env.expect([]).toEqual(jasmineUnderTest.notEmpty());
+    });
+  });
+
+  describe('objectContaining', function () {
+    verifyPasses(function (env) {
+      env.addCustomEqualityTester(function (a, b) {
+        return a.toString() === b.toString();
+      });
+
+      env.expect({a: 1, b: 2}).toEqual(jasmineUnderTest.objectContaining({a: "1"}));
+    });
+
+    verifyFails(function (env) {
+      env.expect({}).toEqual(jasmineUnderTest.objectContaining({a: "1"}));
+    });
+  });
+
+  describe('setContaining', function () {
+    if (jasmine.getEnv().hasFunctioningSets()) {
+      verifyPasses(function (env) {
+        var actual = new Set();
+        actual.add("1");
+        var expected = new Set();
+        actual.add(1);
+
+        env.addCustomEqualityTester(function (a, b) {
+          return a.toString() === b.toString();
+        });
+
+        env.expect(actual).toEqual(jasmineUnderTest.setContaining(expected));
+      });
+    } else {
+      it('pases', function() {
+        jasmine.getEnv().pending('Browser has incomplete or missing support for Sets');
+      });
+    }
+
+    if (jasmine.getEnv().hasFunctioningSets()) {
+      verifyFails(function (env) {
+        env.expect('something').toEqual(jasmineUnderTest.setContaining(new Set()));
+      });
+    } else {
+      it('fails', function() {
+        jasmine.getEnv().pending('Browser has incomplete or missing support for Sets');
+      });
+    }
+  });
+
+  describe('stringMatching', function () {
+    verifyPasses(function (env) {
+      env.expect('foo').toEqual(jasmineUnderTest.stringMatching(/o/));
+    });
+
+    verifyFails(function (env) {
+      env.expect('bar').toEqual(jasmineUnderTest.stringMatching(/o/));
+    });
+  });
+
+  describe('truthy', function () {
+    verifyPasses(function (env) {
+      env.expect(true).toEqual(jasmineUnderTest.truthy());
+    });
+
+    verifyFails(function (env) {
+      env.expect(false).toEqual(jasmineUnderTest.truthy());
+    });
+  });
+});
diff --git a/spec/core/integration/MatchersSpec.js b/spec/core/integration/MatchersSpec.js
index f75aae28..6f81ea04 100644
--- a/spec/core/integration/MatchersSpec.js
+++ b/spec/core/integration/MatchersSpec.js
@@ -261,7 +261,10 @@ describe('Matchers (Integration)', function() {
 
   describe('toBeResolvedTo', function() {
     verifyPassesAsync(function(env) {
-      return env.expectAsync(Promise.resolve('foo')).toBeResolvedTo('foo');
+      env.addCustomEqualityTester(function(a, b) {
+        return a.toString() === b.toString();
+      });
+      return env.expectAsync(Promise.resolve('5')).toBeResolvedTo(5);
     });
 
     verifyFailsAsync(function(env) {
@@ -281,7 +284,10 @@ describe('Matchers (Integration)', function() {
 
   describe('toBeRejectedWith', function() {
     verifyPassesAsync(function(env) {
-      return env.expectAsync(Promise.reject('nope')).toBeRejectedWith('nope');
+      env.addCustomEqualityTester(function(a, b) {
+        return a.toString() === b.toString();
+      });
+      return env.expectAsync(Promise.reject('5')).toBeRejectedWith(5);
     });
 
     verifyFailsAsync(function(env) {
@@ -331,7 +337,10 @@ describe('Matchers (Integration)', function() {
 
   describe('toContain', function() {
     verifyPasses(function(env) {
-      env.expect('foobar').toContain('oo');
+      env.addCustomEqualityTester(function(a, b) {
+        return a.toString() === b.toString();
+      });
+      env.expect(['1', '2', '3']).toContain(2);
     });
 
     verifyFails(function(env) {
@@ -341,7 +350,10 @@ describe('Matchers (Integration)', function() {
 
   describe('toEqual', function() {
     verifyPasses(function(env) {
-      env.expect('a').toEqual('a');
+      env.addCustomEqualityTester(function(a, b) {
+        return a.toString() === b.toString();
+      });
+      env.expect(5).toEqual('5');
     });
 
     verifyFails(function(env) {
@@ -394,8 +406,11 @@ describe('Matchers (Integration)', function() {
   describe('toHaveBeenCalledWith', function() {
     verifyPasses(function(env) {
       var spy = env.createSpy();
-      spy('foo');
-      env.expect(spy).toHaveBeenCalledWith('foo');
+      spy('5');
+      env.addCustomEqualityTester(function(a, b) {
+        return a.toString() === b.toString();
+      });
+      env.expect(spy).toHaveBeenCalledWith(5);
     });
 
     verifyFails(function(env) {
diff --git a/spec/helpers/checkForMap.js b/spec/helpers/checkForMap.js
index 64e32cdc..46e346a8 100644
--- a/spec/helpers/checkForMap.js
+++ b/spec/helpers/checkForMap.js
@@ -1,5 +1,5 @@
 (function(env) {
-  function hasFunctioningMaps() {
+  env.hasFunctioningMaps = function() {
     if (typeof Map === 'undefined') {
       return false;
     }
@@ -36,10 +36,10 @@
     } catch (e) {
       return false;
     }
-  }
+  };
 
   env.requireFunctioningMaps = function() {
-    if (!hasFunctioningMaps()) {
+    if (!env.hasFunctioningMaps()) {
       env.pending('Browser has incomplete or missing support for Maps');
     }
   };
diff --git a/spec/helpers/checkForSet.js b/spec/helpers/checkForSet.js
index 1be8de45..dacb06aa 100644
--- a/spec/helpers/checkForSet.js
+++ b/spec/helpers/checkForSet.js
@@ -1,5 +1,5 @@
 (function(env) {
-  function hasFunctioningSets() {
+  env.hasFunctioningSets = function() {
     if (typeof Set === 'undefined') {
       return false;
     }
@@ -40,10 +40,10 @@
     } catch (e) {
       return false;
     }
-  }
+  };
 
   env.requireFunctioningSets = function() {
-    if (!hasFunctioningSets()) {
+    if (!env.hasFunctioningSets()) {
       env.pending('Browser has incomplete or missing support for Sets');
     }
   };