I try to have my linux system mirror the Users/-folder of my OS/X Apple.

is what I thought would do it.

I then changed it to
tying to deal with my problem:

Every time I start this, rsync does ALL the copying again, just as if all files had changed. Kind defeats the purpose of using rsync, doesn't it?

Can anyone tell me, what the problem is? I guess something like times / owner properties is not correctly syncronized, but I don't know what that might be. Username is the same on both machines. Thanks for your help, I really appreciate it!

Are you sure it's actually copying the files, rather than just checking them? Typically rsync will hash every file to make sure it's unchanged before syncing it.

I'm not familiar with a lot of the rsync flags you're using there. Here's what I usually use:
rsync --compress --verbose --progress --recursive /source/folder/ /destination/folder. The first three flags can be ignored (compress is only useful over the net, and the others let you see what's going on in more detail). If the folder you're backing up has subfolders you'll want the last option though. This tutorial might be useful if you've not seen it before, particularly the section called "Using Rsync Itself".

Hope this helps.

Thank you very much, I tried your options but the result is the same. I am positive it has sth to do with something that for some reason either lets rsync think that the file do not yet exist or a chicking algorithm in file comparison, that uses an information that is not correctly transferred during sync - anybody solved problems like that?

This happens because file attributes like owner, group and modes are not the exactly the same, between the source and target. Check it and you will see !

The owner/group is liked to be different, because you are not running rsync in the local as root, and as regular user you can't change owner/group;

The easiest way to test this is to run both local and remote rsync as root.