acceleration hesitation yet RPM's respond

Thanks for the quick replies. It looks like I wasn't very clear in my description. The engine will hesitate. I mean it falls flat. The tach indicates the RPM's rising as if the engine were responding correctly to my throttle input but the engine totally drops off. It's exactly like a carb would act if it had accelerator pump issues. It gives me the impression that the tach indicates RPM's based on the gas pedal position rather that actual engine rotation speed.

It doesn't matter if the engine is warm or cold. If the RPM's are lower, like below roughly 1,800 or so it will flat spot if I mash the throttle then it will recover quickly. If I'm on the freeway and the RPM's are up and I mash the throttle there will be no hesitation.

I'll have to get it checked I guess. It really doesn't feel like a transaxle or shift issue. When I hit the gas the engine falls flat then kicks in. Yes the tach shows the RPM's rising at that time but the engine is not revving with the transaxle slipping. I don't think the tach is accurately reflecting the engine RPM while this is occurring. It is exactly what happens when a carb'd engine has a flat spot due to the accelerator pump not giving a shot a fuel off idle.

Now you're talkin' guys. You guys are understanding what my impression of the problem is. I've never had a DBW equipped vehicle before and I'm just now starting to read about a hesitation associated with DBW. I would be content if this was my issue but it didn't do it when I bought it this summer. I could borrow a scanner that shows operating perameters but I think the digital readout would not reflect the drop in RPM clearly like an analog tach would.
I haven't come across any common problems with this model car related to the tranny. Are there any? Thanks.
I just noticed my details listed a 2004 green Maxx. That was the car I was looking at when I registered to do research before buying. I ended up with the '05 white Maxx.

seems to be getting worse. Took it to a tranny shop. 1st guy test drove and said it seemed like normal hesitation while downshifting. 2nd guy hooked it up to scanner and drove it. said all looked good.