Summary: The set-valued nonlinear complementarity problems are studied. First, a new auxiliary function is constructed to transform the set-valued nonlinear complementarity problems into fixed point problems. By utilizing the Leary-Schauder fixed point theorem, a sufficient condition is given for the existence of the solution to the set-valued nonlinear complementarity problems. The results generalize some well-known existence theorems. Then, Leary-Schauder fixed point algorithm is established to solve the nonlinear complementarity problems.