Abstract: The purpose of this paper is to introduce the concept of generalized KKM mapping and to obtain some general version of the famous KKM theorem and Ky Fan’s minimax inequality.As applications, we utilize the results presented in this paper to study the saddle .point problem and the existence problem of solutions for a class of quasi-variational inequalities.The results obtained in this paper extend and improve some recent results of [1-6]

Key words: generalized KKM mapping, upper-semicontinuous, γ, -diagonally quasi-convex, saddle point