The paper studies robust M-estimation for generalized linear models, thereby extending results of W. S. Krasker and R. E. Welsch [J. Am. Stat. Assoc. 77, 595-604 (1982; Zbl 0501.62062)] for the linear model. A (quasi-) score function is proposed which possesses certain optimality properties with respect to robustness and efficiency. However, computational efforts seem to grow seriously, compared to ML-estimation. So a one-step estimator is proposed and applied to logistic regression for a medical example.