All controllers have a dead zone for the Sticks, that's the area where the Stick is at 'rest' and no movement happens. If they didn't have this dead zone they would constantly be moving in one direction or another, which is referred to as Stick drift and is a different issue.
Not all controllers use the same type of Sticks, the part on the actual board, and 3rd party controllers are renown for having pretty rotten ones in them anyway, as well as being soldered to the board in a right crappy way which makes removing them a PITA for someone not familiar with desoldering, not to be confused with soldering because desoldering something properly, that is without tearing things up in the process, is by far more difficult to learn and then actually do. If they are the same type as ones used in a 360 or PS2 controller they can be swapped out with those better ones, but not from any of the newer PS3 controllers as those are a completely different type of Stick and work differently.
If the controller has a larger dead zone than normal replacing them could sort it out, or the controller could be designed that poorly and there's nothing you can really do about 'tightening' up the dead zone.
If the controller is drifting removing and reinstalling them sometimes will resolve the issue, or replacing them may be necessary.
In either case, you'll have to take the controller apart and see what they are before it can be determined if they can be swapped or not. Also, the Stick 'Cap' (part you see and touch) may or may not fit on a new Stick either, some of them are designed different in that aspect as well.
Edited by RDC, 22 August 2010 - 05:38 PM.