Probably the spring seat (large rubber bushing) that sits on top of the spring. My car made the same creaking/groaning noise at slow speed. Problem especially happens in cold weather.

Check to see if they are broken by (with the car on the ground) removing the plastic cap on the top of the strut, and GENTLY turning the large strut nut back and forth with a wrench using slight to moderate pressure (not a lot of force, you don't want to break it if it's not already broken). It should feel "spongy" and not spin around. If the nut spins around in either direction than the spring seat is shot.

What happens is the metal collar that is molded into the rubber separates from the rubber. A very common problem on the S80.

If the nut does not spin around then squirt a little oil into the space under the raised washer on top of the strut (under the nut). That will quiet the creaking/groaning noise.

And just a word of caution if you do have to replace the spring seats. Don't buy the cheaper aftermarket one at FCP Groton, it is junk and broke in less than one year. Get the OEM one.

Good luck.
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2001 S80 2.9 (non-turbo), 135K miles