Repetitive processes are characterized by a series of sweeps or passes through a set of dynamics defined over a finite duration where the output produced on any pass acts as a forcing function on, and hence contributes to, the dynamics of the next pass. The resulting control problem is that the output sequence of pass profiles can contain oscillations that increase in amplitude in the pass-to-pass direction. This paper considers bi-directional operation, i.e. a pass is completed and at the end the next one begins but in the opposite direction. In particular, a model for such a process in the case of discrete dynamics is first proposed and new results on stability and control law design for stabilization and performance developed.