Noise when accelerating and decelerating, 97 Buick Century

Hello, I have noticed a noise that occurs when i accelerate in my 97 buick century custom. When slowing down or coming to a stop it gets quieter and then stops until i accelerate again. I can really hear it when i am in the car and the windows are up (ac on or off). It really sounds like it wants to shift into another gear, but, I know from the slight feel of the car shifting that it is shifting properly. What could this noise be. Thanks folks, i appreciate all of your input.:eek7:

is it a whining type noise, similar to a power steering pump when it's low on fluid or going out? if so, you should have the car scanned with a trans capable scan tool and see if you have a P1811 stored. If so, you have transmission issues.