In this article, we propose three tests for general linear hypotheses in generalized linear models with repeated measures using external moment information, including means and (co)variances of outcomes and predictors, as well as previous estimates of model parameters. To this end, we embedded the approach of generalized estimating equations in the generalized method of moments framework. The developed method is capable of reflecting both uncertainty of external information due to estimation by including external variance estimates and uncertainty due to different designs, populations, or procedures by using a set of external values. For block invariant designs, we provide analytic expressions for estimators and some test statistics. Further, for these designs, the dependence structure cancels out, so that our results are valid for every possible of these structures without the need to model it. We investigated the validity and power of the three tests in simulation studies under a variety of conditions. All three tests show nominal type I error rates when correct external information is used and in some cases the use of external information increases the power, even if uncertainties are reflected properly. The three tests have been implemented in the R package exgmm, available on GitHub (https://github.com/MartinJann/exgmm).