My iMac shows double icons on the startscreen. It looks like all icons are copied including the menuicons at the top. Who can help me?

Could be many things, we should start with this...

"Try Disk Utility

1. Insert the Mac OS X Install disc, then restart the computer while holding the C key.

2. When your computer finishes starting up from the disc, choose Disk Utility from the Installer menu at top of the screen. (In Mac OS X 10.4 or later, you must select your language first.)

*Important: Do not click Continue in the first screen of the Installer. If you do, you must restart from the disc again to access Disk Utility.*

3. Click the First Aid tab.

4. Select your Mac OS X volume.

5. Click Repair Disk, (not Repair Permissions). Disk Utility checks and repairs the disk."

http://docs.info.apple.com/article.html?artnum=106214

Then try a Safe Boot, (holding Shift key down at bootup), run Disk Utility in Applications>Utilities, then highlight your drive, click on Repair Permissions, reboot when it completes.

(Safe boot may stay on the gray radian for a long time, let it go, it's trying to repair the Hard Drive.)

If perchance you can't find your install Disc, at least try it from the Safe Boot part onward.

One way to test is to Safe Boot from the HD, (holding Shift key down at bootup), run Disk Utility in Applications>Utilities, then highlight your drive, click on Repair Permissions, Test for problem in Safe Mode...

PS. Safe boot may stay on the gray radian for a long time, let it go, it's trying to repair the Hard Drive

Reboot, test again.

If it only does it in Regular Boot, then it could be some hardware problem like Video card, (Quartz is turned off in Safe Mode), or Airport, or some USB or Firewire device, or 3rd party add-on, Check System Preferences>Accounts>Login Items window to see if it or something relevant is listed.

Check the System Preferences>Other Row, for 3rd party Pref Panes.