OK - I uninstalled all previous installed SQL Server and Visual Studio parts I could find in the Control Panel. Still no success.
This was beginning to be annoying, so I deleted all SQL Server and Visual Studio fils and folders. Hrmf - still the same error while installing SQL2008R2.
This morning I found the solution in the blog post "Rule "Previous releases of Microsoft Visual Studio 2008" failed" by Mark Smith at LessThanDot.
The trick is to start the installation with the Windows Shell statement
setup.exe /ACTION=install /SkipRules=VSShellInstalledRule
The installation finished with success and I can continue on working with the latest version of SQL Server.