diff --git a/packages/playwright-core/src/client/network.ts b/packages/playwright-core/src/client/network.ts
index 74b8df9367..cb18681ccf 100644
--- a/packages/playwright-core/src/client/network.ts
+++ b/packages/playwright-core/src/client/network.ts
@@ -97,6 +97,7 @@ export class Request extends ChannelOwner<channels.RequestChannel> implements ap
 
   constructor(parent: ChannelOwner, type: string, guid: string, initializer: channels.RequestInitializer) {
     super(parent, type, guid, initializer);
+    this.markAsInternalType();
     this._redirectedFrom = Request.fromNullable(initializer.redirectedFrom);
     if (this._redirectedFrom)
       this._redirectedFrom._redirectedTo = this;
@@ -645,6 +646,7 @@ export class Response extends ChannelOwner<channels.ResponseChannel> implements
 
   constructor(parent: ChannelOwner, type: string, guid: string, initializer: channels.ResponseInitializer) {
     super(parent, type, guid, initializer);
+    this.markAsInternalType();
     this._provisionalHeaders = new RawHeaders(initializer.headers);
     this._request = Request.from(this._initializer.request);
     Object.assign(this._request._timing, this._initializer.timing);
diff --git a/tests/library/trace-viewer.spec.ts b/tests/library/trace-viewer.spec.ts
index 0daf06298a..7e64c62156 100644
--- a/tests/library/trace-viewer.spec.ts
+++ b/tests/library/trace-viewer.spec.ts
@@ -1444,6 +1444,24 @@ test('should not record route actions', {
   ]);
 });
 
+test('should not record network actions', {
+  annotation: { type: 'issue', description: 'https://github.com/microsoft/playwright/issues/33558' },
+}, async ({ page, runAndTrace, server }) => {
+  const traceViewer = await runAndTrace(async () => {
+    page.on('request', async request => {
+      await request.allHeaders();
+    });
+    page.on('response', async response => {
+      await response.text();
+    });
+    await page.goto(server.EMPTY_PAGE);
+  });
+
+  await expect(traceViewer.actionTitles).toHaveText([
+    /page.goto.*empty.html/,
+  ]);
+});
+
 test('should show baseURL in metadata pane', {
   annotation: { type: 'issue', description: 'https://github.com/microsoft/playwright/issues/31847' },
 }, async ({ showTraceViewer }) => {
diff --git a/tests/playwright-test/test-step.spec.ts b/tests/playwright-test/test-step.spec.ts
index f0e3099540..ac6845eeae 100644
--- a/tests/playwright-test/test-step.spec.ts
+++ b/tests/playwright-test/test-step.spec.ts
@@ -1406,9 +1406,7 @@ pw:api    |page.setContent @ a.test.ts:5
 test.step |custom step @ a.test.ts:6
 pw:api    |  page.waitForResponse @ a.test.ts:7
 pw:api    |  page.click(div) @ a.test.ts:13
-pw:api    |  response.text @ a.test.ts:8
 expect    |  expect.toBeTruthy @ a.test.ts:9
-pw:api    |  response.text @ a.test.ts:15
 expect    |expect.toBe @ a.test.ts:17
 hook      |After Hooks
 fixture   |  fixture: page
@@ -1416,6 +1414,42 @@ fixture   |  fixture: context
 `);
 });
 
+test('reading network request / response should not be listed as step', {
+  annotation: { type: 'issue', description: 'https://github.com/microsoft/playwright/issues/33558' }
+}, async ({ runInlineTest, server }) => {
+  const result = await runInlineTest({
+    'reporter.ts': stepIndentReporter,
+    'playwright.config.ts': `module.exports = { reporter: './reporter' };`,
+    'a.test.ts': `
+      import { test, expect } from '@playwright/test';
+      test('waitForResponse step nesting', async ({ page }) => {
+        page.on('request', async request => {
+          await request.allHeaders();
+        });
+        page.on('response', async response => {
+          await response.text();
+        });
+        await page.goto('${server.EMPTY_PAGE}');
+      });
+      `
+  }, { reporter: '', workers: 1, timeout: 3000 });
+
+  expect(result.exitCode).toBe(0);
+  expect(stripAnsi(result.output)).toBe(`
+hook      |Before Hooks
+fixture   |  fixture: browser
+pw:api    |    browserType.launch
+fixture   |  fixture: context
+pw:api    |    browser.newContext
+fixture   |  fixture: page
+pw:api    |    browserContext.newPage
+pw:api    |page.goto(${server.EMPTY_PAGE}) @ a.test.ts:10
+hook      |After Hooks
+fixture   |  fixture: page
+fixture   |  fixture: context
+`);
+});
+
 test('calls from page.route callback should be under its parent step', {
   annotation: { type: 'issue', description: 'https://github.com/microsoft/playwright/issues/33186' }
 }, async ({ runInlineTest, server }) => {