2002 STR when accelerating gently at 5th and 6th gear it seems like car wants to jump ahead and then slows down.It is not smooth as I would expect.When accelerating fast no probs.Any Ideas?
Hope my description explains a bit

 

Sounds like it is upshifting into overdrive too quick. Are you in sport mode? Probably a simple matter of your trans adaptation. Looks like you may not have owned this car too long, it will likely learn what you like to do in this situation after a short period of time.

 

Just have it for a week now.
Not in a sport mode.Need to see how it goes then.Hopefully car will get to like me in a bit

 

Sounds wrong.

Long list of possible causes from a failing sensor to autobox with wrong oil level.

I'd start by monitoring fuel trims closely, at idle, at 2500rpm (parked) and then as you do the relevant actions that cause the effect.

If that reveals nothing I think I'd check RPM, MAF and whatever else seems hopeful!

 

Jagv8- I know you're a tech and that is likely the best way to go about it, but the car is ten years old an the guy has had it 2 weeks. I've been around the block with S-types myself and some simple driving may fix this little idiosyncrasy right up. Not sayin you're wrong, just saying give it a couple weeks before dissecting the fuel trim

 

I'd start checking now. Very cheap (about a tenner - that's $15) to get an adequate OBD tool.

In case it's short on ZF oil it could be very bad news.

 

Thing is when accelerating hard all is ok.
Anyway will try to get it check out asap.My local jag dealer are horrible in customers service.Wanted to book for suprcharger belt change,health check and diagnostic - hard to get them to call back.Probably don't want to spend tousands and they treat me as not worthy to be bothered with-nice one