This article studies a dual problem corresponding to a generalized equilibrium problem (GEP). In the first two sections the authors introduce the equilibrium problem to be studied and several known preliminary results and theorems are outlined. The third section contains the main contribution of this paper and it presents the dual problem of the GEP and proves several theorems relating to the relationship of the solution to the saddle points of a Lagrangian function. The article concludes with a lost of relevant references.