In the context of polytomous regression, as with any generalized linear model, robustness issues are well documented. Existing robust estimators are designed to protect against misclassification, but do not protect against outlying covariates. It is shown that this can have a much bigger impact on estimation and testing than misclassification alone. To address this problem, two new estimators are introduced: arobust generalized linear model-type estimator and an optimal B-robust estimator, together with the corresponding Wald-type and score-type tests. Asymptotic distributions and variances of these estimators are provided as well as the asymptotic distributions of the test statistics under the null hypothesis. Acomplete comparison of the proposed new estimators and existing alternatives is presented. This is performed theoretically by studying the influence functions of the estimators, and empirically through simulations and applications to a medical dataset.