This paper extends some results involving linear inner systems to the nonlinear case. In thsi regard, the arithmetic of nonlinear inner systems is developed further and some new connections with nonlinear spectral and all-pass factorization and control theory are discussed. In particular, explicit formulas for the (state space) realizations of nonlinear inner systems in terms of the components of extremal spectral factors is provided. Relationships between inner systems and process control, geometric control and H-infinity control are also discussed.