Well, the voltage changes a little bit when you turn them on, and varies some with the temperature of the die.
As long as you drive them within spec, though, it stays fairly constant. If you drive them too hard, however, all sorts of weird things can happen. Sometimes they won't light at all unless you put a lot of voltage through them, sometimes they light dimly at a given voltage.
But as a rule, when treated with love and kindness, they're fairly stable.
