I thought wine might run better from a real windows install. So I resized my partitions to free some 8 GB space. Unfortunately the partitioning software was not really great as I lost one of my partitions (the one where I had stored all of my downloads...). So I decided to go for a clean start and formatted the whole hard disk. First I partitioned the disk using cfdisk.
I reinstalled Acrobat 5 to run it under wine. It didn't work. The reason appeared to be again a plugin: DocBox.api. After removing it everything went smoothly. Already before (using RedHat 9) I have had trouble with a Acrobat plugin (it was WebPDF.api at that time). Most manipulation of pdf files can be easily done with Linux tools, but one thing is tricky: cropping already existing pdf files. That's why I need Acrobat.
Adobe Illustrator didn't want to start up under wine, because it couldn't find the file AI90Res.dll. This file is located after the Illustrator install in:
~/.cxoffice/dotwine/fake_windows/Program Files/Adobe/Illustrator 10/Support Files/Contents/Windows/System
I just moved it up one directory and everything started working.