The paper deals with approximate methods for solving ill-posed problems with nonselfadjoint bounded linear operators acting in a Hilbert space. The case of nonexact right hand side is considered.Aposteriori choice of a method parametern(δ) depending on the error of data is based on the value of the residuum. The convergence of approximate solution when δ → 0 is investigated and the parametern(δ) is estimated. The simple iteration method is considered in more detail.