We introduce the notion of a parametrized family (H_p)_{p Î P}of hybrid systems, and consider questions of reachability in the systems H_p as the parameter p ranges over P. Under the assumption of a uniform (as p ranges over P) finite bound on the number of discrete transitions associated to the individual systems H_p, the notion of reachability is first-order (in the sense of mathematical logic) and uniform in the parameter p. Techniques from logic can then be used to analyze computational questions associated to the family of systems.