  In this paper we prove an existence result for a general class of
hemivariational inequalities systems using the Ky Fan version of KKM theorem
(1984) or the Tarafdar fixed point theorem (1987). As application we give an
infinite dimensional version for existence result of Nash generalized
derivative points introduced recently by Krist\'{a}ly (2010) and also we give
an application to a general hemivariational inequalities system.
