1997 g.m has trouble moving when cold

i ahve a 1997 grand marquis with about 190k. Recntly when i start it and let it idle down and oput it into drive and press the gas the rpms go down and it wont really move. once I get to 20 mph itll go fine. but when i press the gas it like studders then it goes. what could be wrong?

When you hit the gas, the RPMs go down and not up? If they went up, I'd suspect a bad solenoid or worn out clutch for first gear. You'd be in second gear a little before 20MPH which is when you say you accelerate fine which is why I suspect something with the first gear in your transmission.