Bathtub Faucet Valve Stem

I am trying to replace the washers in my bathtub faucets, but despite removing all of the nuts etc around the stem, I cannot remove the stem to get to the washer.

It appears to be a regular compression set up, but once everything is off, the stem just spins, but cannot be removed. You can wiggle it up and down and even pull it to seat the washer, but I can't figure out how to get it out to replace it. Any suggestions would be greatly appreciated.

You probably have just removed the packing nut. There is probably another one deeper in the wall.

faucet

What do you mean by "pull it out to seat the washer"? Is the hole in the wall large enough? Something inside it may have swollen or become displaced and you just have to pull harder. But do anything carefully, because if you break it and cannot get it out you will not have any water until you do. Pictures of the unit might help us see what your problem is.