I have difficulties in cleanly shutdown or logout from within kde, as nothing happens when I click any buttons on the kdm logout window.
The kdm logout window just disappears and no shutdown, no logout happens.

In the meantime I found some more strange things: there is absolutely way to logout by the first attempt. By the second attempt I can succeed if (and only if) I hold down the left mouse button on the OK button of the kdm logout window for cca. 3-5 seconds before releasing it. If I release it before 3s or after 5s then it will fail again, and no further logout attempts will be successful.

Shutdown from a konsole window with the "shutdown -h" command always works.

Could you help me how to achieve a reliable logout or shutdown by kdm?

Which version of KDE are you using? When did you install it? When did this problem begin? And what system are you using?

It is a 6 months-old SuSe 9.0 installation with kde 3.2.1, in a local network environment.

These problems began maybe 3 months ago, but I could not find any reason for them, and I tolerated it so far.

That is pretty weird. I think this is probably a bug in this version of KDE. It may be worthwhile to upgrade, if it's really annoying.