The necessary conditions for local extremum in 2-regular problems are studied. The necessary conditions for an extremum that uses the Lagrangian function L are generally invalid. The generalization gives no additional information on the irregular situation, since the corresponding first-order necessary condition in automatically satisfied with λ= 0, irrespective of f. The first and second-order necessary conditions for a local extremum were obtained by using the Lagrange functions, in the irregular case for a problem with equality constrain. The necessary conditions for a local extremum are first-order conditions, as they use only the first derivatives of the objective function f. The function f is twice Frechet differentiable at x and the function F is thrice Frechet differentiable at the second order necessary conditions.