Regularization methods for the solution of nonlinear complementarity problems are standard methods for the solution of monotone complementarity problems and possess strong convergence properties. In this paper, we replace the monotonicity assumption by a P-0-function condition. We show that many properties of regularization methods still hold for this larger class of problems. However, we also provide some counterexamples which indicate that not all results carry over from monotone to P-0-function complementarity problems.