Friedman test can be used only for unreplicated complete block design. It sounds like your data won't fit into this design.

If it makes sense to take the difference between the time points and then run a Mann-Whitney (or Kruskal-Wallis for more groups), then that would be an acceptable approach.

For more complicated nonparametric designs, there is the technique of aligned ranks. ARTool appears to be the premier (and free!) software for this. I have almost no experience with it, but it seems to accommodate most common designs including those with repeated measures. It can be used as an R package, or apparently as a stand-alone Windows program.

Let me also cross-reference this thread, in case it helps:

https://www.researchgate.net/post/How_to_analyse_non_normal_data_with_2_factors_which_dont_conform_to_a_non_parametric_Friendmans_test

Thank you for your quick and helpful answer! I think I will take the difference and then run a Mann-Whitney-U-Test.

Although I have also read your post regarding generalized linear modeling, I assume this is rather a solution for not normally distributed data, isn't it? My problem was that the group variances weren't homogeneous and the sample sizes differed from each other (73/37).

Well, generalized linear models are for data that we don't suspect come from a normal distribution to begin with. For example, count data is discrete and left-limited (e.g. not less zero), so we wouldn't expect it to be normally distributed. Likewise concentrations of a water pollutant are left-limited and likely to be log-normally distributed.

I'll also note that there are some traditional non-parametric tests that can handle heteroscedasticity, such as Welch's anova and white-adjusted linear models.

P.S. Be sure to understand the hypothesis tested by Mann-Whitney. It tests the median only under certain conditions.

Thanks!