In this paper, using a power series methodology a design procedure applicable to analytic nonlinear plants is described. The technique used is a generalization of the linear H-infinity theory. In contrast to previous work on this topic ([Indiana J. Math., 36 (1987), pp. 693-709], [Oper. Theory Adv. Appl., 41 (1989), pp. 255-277], [SIAM J. Control Optim., 27 (1989), pp. 842-860]), the authors are now able to incorporate explicitly a causality constraint into the theory. In fact, it is shown that it is possible to reduce a causal optimal design problem (for nonlinear systems) to a classical interpolation problem solvable by the commutant lifting theorem [Harmonic Analysis of Operators on Hilbert Space, North-Holland, Amsterdam, 1970], [The Commutant Lifting Approach to Interpolation Problems, Birkhauser, Boston, 1990].