diff --git a/.travis.yml b/.travis.yml
index b0f0775f..a4426161 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -50,3 +50,4 @@ matrix:
       if: type != pull_request
       addons:
         sauce_connect: true
+    - env: JASMINE_LONG_PROPERTY_TESTS=y
diff --git a/package.json b/package.json
index e2ba236f..bc602f6f 100644
--- a/package.json
+++ b/package.json
@@ -30,6 +30,7 @@
     "ejs": "^2.5.5",
     "eslint": "^5.16.0",
     "express": "^4.16.4",
+    "fast-check": "^1.21.0",
     "fast-glob": "^2.2.6",
     "grunt": "^1.0.4",
     "grunt-cli": "^1.3.2",
diff --git a/spec/property/matchersUtilSpec.js b/spec/property/matchersUtilSpec.js
new file mode 100644
index 00000000..384a1f14
--- /dev/null
+++ b/spec/property/matchersUtilSpec.js
@@ -0,0 +1,69 @@
+describe('matchersUtil -- property tests', function() {
+  'use strict';
+  var fc = require('fast-check');
+
+  function basicAnythingSettings() {
+    return {
+      key: fc.oneof(fc.string(), fc.constantFrom('k1', 'k2', 'k3')),
+      // Limiting depth & number of keys allows fast-check to try
+      // a lot more scalar values.
+      maxDepth: 2,
+      maxKeys: 5,
+      withBoxedValues: true,
+      withMap: true,
+      withSet: true
+    };
+  }
+
+  function numRuns() {
+    var many = 5000000;
+
+    // Be thorough but very slow when specified (usually on CI).
+    if (process.env.JASMINE_LONG_PROPERTY_TESTS) {
+      console.log(
+        'Using',
+        many,
+        'runs of fc.assert because JASMINE_LONG_PROPERTY_TESTS was set. This may take several minutes.'
+      );
+      return many;
+    } else {
+      return undefined;
+    }
+  }
+
+  describe('equals', function() {
+    it('is symmetric', function() {
+      fc.assert(
+        fc.property(
+          fc.anything(basicAnythingSettings()),
+          fc.anything(basicAnythingSettings()),
+          function(a, b) {
+            return (
+              jasmineUnderTest.matchersUtil.equals(a, b) ===
+              jasmineUnderTest.matchersUtil.equals(b, a)
+            );
+          }
+        ),
+        {
+          numRuns: numRuns(),
+          examples: [[0, 5e-324]]
+        }
+      );
+    });
+
+    it('is reflexive', function() {
+      var anythingSettings = basicAnythingSettings();
+      anythingSettings.withMap = false;
+      fc.assert(
+        fc.property(fc.dedup(fc.anything(anythingSettings), 2), function(
+          values
+        ) {
+          return jasmineUnderTest.matchersUtil.equals(values[0], values[1]);
+        }),
+        {
+          numRuns: numRuns()
+        }
+      );
+    });
+  });
+});
diff --git a/spec/support/jasmine-browser.js b/spec/support/jasmine-browser.js
index 41c9e703..bbc9c4ac 100644
--- a/spec/support/jasmine-browser.js
+++ b/spec/support/jasmine-browser.js
@@ -15,7 +15,7 @@ module.exports = {
     '**/*.js'
   ],
   specDir: 'spec',
-  specFiles: ['**/*[Ss]pec.js', '!npmPackage/**/*'],
+  specFiles: ['**/*[Ss]pec.js', '!npmPackage/**/*', '!property/**/*'],
   helpers: [
     'helpers/asyncAwait.js',
     'helpers/BrowserFlags.js',
diff --git a/spec/support/jasmine.json b/spec/support/jasmine.json
index 033207ec..6ce73409 100644
--- a/spec/support/jasmine.json
+++ b/spec/support/jasmine.json
@@ -2,6 +2,7 @@
   "spec_dir": "spec",
   "spec_files": [
     "core/**/*[Ss]pec.js",
+    "property/**/*[Ss]pec.js",
     "npmPackage/**/*[Ss]pec.js"
   ],
   "helpers": [