A new procedure of robust control design is presented for nonlinear systems with parametric uncertainty and disturbance. This nonlinear optimization-based approach can design robust nonlinear controllers of widely different structures and arbitrary complexity. By taking the worst-case design approach, a minimax optimization problem is formulated. A number of state-of-the-art optimization procedures are explored as possible candidates for minimaximization. It is determined that the tools of non-smooth analysis and optimization are the most useful for the efficient solution of practical size worst-case design problems. Included in the paper are the significant details of a special two-tier structured minimax programming algorithm implemented in this work. The overall algorithm is used in solving two robust nonlinear control design problems. The controller designs produced by the minimax optimization algorithm are discussed and the performance of the controllers is studied by simulations.