I recently bought a Centurion Sport DLX, some old school road bike from the early eighties. The bike has this weird habit of trying to force me to bike straight. What I mean by this is that when I turn, I have to overcome some kind of resistance to turn away from straight, but this resistance disappears as I turn away. It kind of feels like a cabinet door that snaps shut. The front steering keeps on trying to sink back into facing straight. It's hard to describe.

I've narrowed it down to some kind of fork-headset relationship. I've ruled out the handlebars, and associated cables, after taking it out and the front wheel still acting in this manner. I'm a bit reluctant to undo the headset and fork unless I have to.

Has anybody else ever seen/felt an issue with their steering like this? Anybody know what I have to remove/replace to stop this?