It has been argued that the existence of faster than light particles in the context of special relativity would imply the possibility to influence the past, and that this would lead to paradox. In this paper I argue that such conclusions cannot safely be drawn without consideration of the equations of motion of such particles. I show that such equations must be non-local, that they can be deterministic, and that they can avoid the suggested paradoxes. I also discuss conservation of (...) energymomentum, and how instantaneous action at a distance can avoid similar paradoxes. *I am most grateful for helpful comments made by John Earman, and especially John Norton, who is responsible for anything that makes sense in this paper. I am also grateful for the reception of a Mellon postdoctoral fellowship, which supported me whilst doing the research for this paper. (shrink)