A nonlinear operator equation is investigated when the Hadamard correctness conditions are not met. For construction of a stable method for solving equation, we suggest two-stage method. It includes the modified Tikhonov regularization and the modified iterative Gauss–Newton process for approximation of a solution of the regularized equation. The convergence of iterations and the strong Fejer property of the process are proved. On the class of sourcewise representable functions the order optimal estimate of the error for two-stage method is established.