A non-linear system Σ has a right fraction representation if it can be represented as Σ = PQ−1, where P and Q are stable systems, and it has a left fraction representation if it can be represented as Σ = G−1T, where G and T are stable systems. We develop here a theory of right and of left fraction representations for discrete-time non-linear systems with bounded input sequences. We indicate the connection between fraction representations and the stabilization problem for non-linear systems.