Singular modes of a nonlinear system in the case of multiple maxima

The sufficient conditions [1] of a strong minimum for singular modes in the case of a linear and involutional system of multiple maxima is extended to the general case of a system of multiple maxima which can also be nonlinear. Since the set of velocities is limited the system of multiple maxima need not be involutional. The results cover the important case of the path consisting of singular and nonsingular parts.