Most biomedical research is carried out using longitudinal studies. The method of generalized estimating equations (GEEs) introduced by Liang and Zeger [Longitudinal data analysis using generalized linear models, Biometrika 73 (1986), pp. 13--22] and Zeger and Liang [Longitudinal data analysis for discrete and continuous outcomes, Biometrics 42 (1986), pp. 121--130] has become a standard method for analyzing non-normal longitudinal data. Since then, a large variety of GEEs have been proposed. However, the model diagnostic problem has not been explored intensively. Oh et al. [Modeldiagnostic plots for repeated measures data using the generalized estimating equations approach, Comput. Statist. Data Anal. 53 (2008), pp. 222--232] proposed residual plots based on the quantile--quantile (Q--Q) plots of the χ-super-2-distribution for repeated-measures data using the GEE methodology. They considered the Pearson, Anscombe and deviance residuals. In this work, we propose to extend this graphical diagnostic using a generalized residual. A simulation study is presented as well as two examples illustrating the proposed generalized Q--Q plots.