Related t o a concept of Gol'stejn/Tretjakov (1974) for convex programming we investigate a class of modified Lagrangians for nonconves problems. We formulate local duality and sensitivity results. Theorem 10 containing the main result of the paper allows to estimate the rate of convergence for a, class of multiplier methods. Some special results shown by BLT-s (1972), Poljak/Tretjakov (1973) and Bertseeas (1975), (1976) follow from t h e generally proved theorems of this paper.