In this paper we introduce and develop robust versions of quasi-likelihood functions for model selection via an analysis-of-deviance type of procedure in generalized linear models and longitudinal data analysis. These robust functions are built upon natural classes of robust estimators and can be seen as weighted versions of their classical counterparts. The asymptotic theory of these test statistics is stuided and their robustness properties are assessed for both generalized linear models and longitudinal data analysis. The proposed class of test statitstics yields reliable inference even under model contamination. The analysis of a real data set completes the article.