I purchased a used 2004 Passat TDI and drove it 1250 miles. The problem started about 300 miles into the trip. I would try and accelerate quickly and it would hesitate and shudder. When I let up on the throttle it would accelerate without the shudder. I thought maybe it was the fuel filter and added some condtioner to it, but this did not seem to help. The car ran smooth at 73 mph and I did notice a shudder once and while when climbing hills. The car has 56000 miles on it and I am not sure what mainenance has been done to it. Does the transmission need to be replaced?

Try changing the fluid and filter. I know you may not like to hear this but, it's best to have it serviced at the dealership. VW uses their own transmission fluid and any other fluid may just ruin the transmission, when there might not be a problem other than just a cleaning. Hope this helps!
Franco

Thank you for the reply. I talked to my neighbor who is a mechanic and had a class on the 2.0 TDI engine. He checked all the service manuals and thinks that the computer needs to be reprogrammed. He is not able to do this where he works, so off to the dealer I go. I hope it is not too painful of a trip.