diff --git a/package-lock.json b/package-lock.json
index 2d2cfcec265f..0c60ac3a95ef 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -14323,9 +14323,9 @@
       "integrity": "sha1-vIAEFkaRkjp5/oN4u+s9ogF1OOw="
     },
     "tslint": {
-      "version": "5.4.3",
-      "resolved": "https://registry.npmjs.org/tslint/-/tslint-5.4.3.tgz",
-      "integrity": "sha1-dhyEArgONHt3M6BDkKdXslNYBGc=",
+      "version": "5.5.0",
+      "resolved": "https://registry.npmjs.org/tslint/-/tslint-5.5.0.tgz",
+      "integrity": "sha1-EOjas+MGH6YelELozuOYKs8gpqo=",
       "dev": true,
       "requires": {
         "babel-code-frame": "6.22.0",
@@ -14345,15 +14345,6 @@
           "resolved": "https://registry.npmjs.org/colors/-/colors-1.1.2.tgz",
           "integrity": "sha1-FopHAXVran9RoSzgyXv6KMCE7WM=",
           "dev": true
-        },
-        "tsutils": {
-          "version": "2.6.0",
-          "resolved": "https://registry.npmjs.org/tsutils/-/tsutils-2.6.0.tgz",
-          "integrity": "sha1-5emceaiszTl3zhjYP98dI1psLrs=",
-          "dev": true,
-          "requires": {
-            "tslib": "1.7.1"
-          }
         }
       }
     },
diff --git a/package.json b/package.json
index 66a30551e585..361f4306e0d0 100644
--- a/package.json
+++ b/package.json
@@ -113,7 +113,7 @@
     "stylelint": "^7.12.0",
     "ts-node": "^3.0.4",
     "tsconfig-paths": "^2.2.0",
-    "tslint": "~5.4.3",
+    "tslint": "~5.5.0",
     "tsutils": "^2.6.0",
     "typescript": "~2.2.1",
     "uglify-js": "^2.8.14",
diff --git a/src/cdk/rxjs/rx-chain.ts b/src/cdk/rxjs/rx-chain.ts
index 57b126cead24..0d6d25e7f190 100644
--- a/src/cdk/rxjs/rx-chain.ts
+++ b/src/cdk/rxjs/rx-chain.ts
@@ -24,7 +24,7 @@ export class RxChain<T> {
    * Starts a new chain and specifies the initial `this` value.
    * @param context Initial `this` value for the chain.
    */
-  static from<T>(context: Observable<T>): StrictRxChain<T> {
+  static from<O>(context: Observable<O>): StrictRxChain<O> {
     return new RxChain(context);
   }
 
diff --git a/src/lib/core/style/focus-origin-monitor.ts b/src/lib/core/style/focus-origin-monitor.ts
index 83d7c0af94b0..418777bec907 100644
--- a/src/lib/core/style/focus-origin-monitor.ts
+++ b/src/lib/core/style/focus-origin-monitor.ts
@@ -84,9 +84,9 @@ export class FocusOriginMonitor {
     }
     // Check if we're already monitoring this element.
     if (this._elementInfo.has(element)) {
-      let info = this._elementInfo.get(element);
-      info!.checkChildren = checkChildren;
-      return info!.subject.asObservable();
+      let cachedInfo = this._elementInfo.get(element);
+      cachedInfo!.checkChildren = checkChildren;
+      return cachedInfo!.subject.asObservable();
     }
 
     // Create monitored element info.
diff --git a/tools/gulp/tasks/docs.ts b/tools/gulp/tasks/docs.ts
index 840ddbc17277..bf3e8adbe10e 100644
--- a/tools/gulp/tasks/docs.ts
+++ b/tools/gulp/tasks/docs.ts
@@ -93,9 +93,9 @@ task('markdown-docs', () => {
  */
 task('highlight-examples', () => {
   // rename files to fit format: [filename]-[filetype].html
-  const renameFile = (path: any) => {
-    const extension = path.extname.slice(1);
-    path.basename = `${path.basename}-${extension}`;
+  const renameFile = (filePath: any) => {
+    const extension = filePath.extname.slice(1);
+    filePath.basename = `${path.basename}-${extension}`;
   };
 
   return src('src/material-examples/**/*.+(html|css|ts)')