This paper studies the realizability property of bilinear input-output (i/o) models in the classical state space form. Constraints on the parameters of the bilinear i/o model are suggested that lead to realizable models. The complete list of 2nd and 3rd order realizable input-output bilinear models together with the corresponding state equations is given. In the general case some subclasses of realizable bilinear models together with their state-space realizations are presented, including the diagonal bilinear model and the special subclass of the superdiagonal bilinear model.