Now I've cloned my System from the internal SSD to an external HD and boot from that HD and the problem persists. So the issue seems not related to the SSD as I thought first.
Again a description of the misbehaviour: When I gave the save command jedit needs 5 seconds to save the file (until the red Floppy Disc Symbol disappears).

Maybe You should try to delete (or rename) Your settings directory...

You mean that folder called jedit and lives in ~/Libary/?
I already tried this- no difference...
Are there other jedit-related files somewhere?

Ah, You've already mentioned

Then You may ensure that You have trashed the folder that really is used by jEdit: Please chose "Utilities -> Settings Directory". The topmost list item is the name of the current Settings Directory.

Regarding Your question:
In jEdit's program directory is a subdirectory "properties". At startup jEdit processes all files in there with extension ".props".
Also at startup all scripts in the subdirectory "startup" are processed.

jEdit is pointing exactly to that folder I mentioned before.
I also made a new user accout and installed a new jEdit on that- the same delay problem- that means that there is something wrong systemwide, does'nt it?

Maybe you could find another Java application to test a save operation.

Also, I wonder what You've changed to Your system, when You replaced the hard disk...

Can you suggest a little java app which resorts to the save java sources as jedit does?

I could not remember changing anything beside moving big sample librarys to external harddiscs to make the whole OS Volume smaller...

I've found out that the new versions of "Vienna Instruments" respectively "Vienna Ensemble" which is a sample player software for classical instruments did cause the bug.
It is very unlikely that someone else is using the combination of "Vienna Symphonic Library" and jEdit, but if yes be aware!

@Robert: Thank you for your help/ not letting me alone...