diff --git a/lib/element.ts b/lib/element.ts
index ee6d3d5af..0bac0a4ba 100644
--- a/lib/element.ts
+++ b/lib/element.ts
@@ -652,13 +652,17 @@ export class ElementArrayFinder extends WebdriverWebElement {
    */
   map<T>(mapFn: (elementFinder?: ElementFinder, index?: number) => T | any):
       wdpromise.Promise<T[]> {
-    return this.asElementFinders_().then<T[]>((arr: ElementFinder[]) => {
-      let list = arr.map((elementFinder?: ElementFinder, index?: number) => {
-        let mapResult = mapFn(elementFinder, index);
-        // All nested arrays and objects will also be fully resolved.
-        return wdpromise.fullyResolved(mapResult) as wdpromise.Promise<T>;
+    const finders = this.asElementFinders_();
+    // execute mapFn one-at-a-time to prevent concurrent webdriver requests
+    return finders.then(arr => {
+      let promise = finders.then(() => []);
+      arr.forEach((elementFinder, index) => {
+        promise = promise.then(result => {
+          const mapResult = wdpromise.fullyResolved(mapFn(elementFinder, index));
+          return mapResult.then(mr => result.concat([mr]));
+        });
       });
-      return wdpromise.all(list);
+      return promise;
     });
   };
 
diff --git a/spec/ts/basic/element_spec.ts b/spec/ts/basic/element_spec.ts
index 18ca6a7da..d813c49d2 100644
--- a/spec/ts/basic/element_spec.ts
+++ b/spec/ts/basic/element_spec.ts
@@ -184,3 +184,28 @@ describe('ElementFinder', function() {
     await expect(usernameInput.equals(name)).toEqual(false);
   });
 });
+
+describe('ElementArrayFinder', function() {
+  it('should be able to invoke #map on many elements', async () => {
+    // running map callbacks concurrently would crash webdriver as it can't handle
+    // concurrent requests (at least no with Crome on MacOS)
+    await browser.get('index.html#/form');
+    await element.all(by.css('*')).map(elem => elem.getText().then(_ => {}));
+    // no real expectation, the real target is that we get here without exceptions
+  });
+
+  it('should invoke ElementArrayFinder.map callbacks sequentially', async () => {
+    await browser.get('index.html#/form');
+    let running = 0;
+    let highwater = 0;
+    await element.all(by.css('*')).map(elem => Promise.resolve()
+      .then(() => {
+        running++;
+        highwater = Math.max(running, highwater);
+        return new Promise(resolve => setTimeout(resolve, 1));
+      })
+      .then(() => {running--;})
+    );
+    expect(highwater).toEqual(1);
+  });
+});