Summary: Iterative regularization methods for nonlinear ill-posed equations of the form

$F\left(x\right)=y$, where

$F:D\left(F\right)\subset X\to Y$ is an operator between Hilbert spaces

$X$ and

$Y$, usually involve calculation of the Fréchet derivatives of

$F$ at each iterate and at the unknown solution

${x}^{\u2020}$. In this paper, we suggest a modified form of the generalized Gauss-Newton method which requires the Fréchet derivative of

$F$ only at an initial approximation

${x}_{0}$ of the solution

${x}^{\u2020}$. The error analysis for this method is done under a general source condition which also involves the Fréchet derivative only at

${x}_{0}$. The conditions under which the results of this paper hold are weaker than those considered by

*B. Kaltenbacher* [Numer. Math. 79, No. 4, 501–528 (1998;

Zbl 0908.65042)] for an analogous situation for a special case of the source condition.