In this talk, a method for designing strategies for either guaranteed escape of the evaders or guaranteed capture of all evaders by the pursuers, in a game with an arbitrary number of players, will be presented. The players are modeled as nonlinear dynamic systems. The methodology is based on differential inequalities related to the comparison principle and Liapunov-like analysis. The Liapunov-type functions, used to design players strategies, represent continuously differentiable upper and lower approximations of the minimum and maximum function of an arbitrary number of arguments. As an illustration of the proposed methodology, some examples with multiple nonidentical nonholonomic players will be presented. Finally, an idea of how to use this approach for a more general class of differential games will be discussed.