Summary: We investigate the inexact Tikhonov and proximal point regularization methods for pseudomonotone equilibrium problems. In this case, the regularized subproblems might not be strongly monotone, even not pseudomonotone. However, any iterative sequence of the regularized subproblems tends to the same solution, which, for the Tikhonov method, is the projection of the starting point onto the solution set of the original problem. This convergence result suggests algorithms for finding the limit point of the Tikhonov regularization method. An application to multivalued pseudomonotone variational inequalities is discussed.