Can one yse statistical sig of an interaction between variables, with non-parametric tests?

I have had to use non-parametric tests on my data, as various umptions of parametric tests have been vioated (for some variables, it's non-normal distributions, for another geneity of variance is violatated). I have small and uneven samples too. I have run the obvious between and within-subjects yses and I understand the results and can report them OK. However, my graphs of the data show clear (and emprically interesting), albeit small, interactions between some of the variables. If I were able to run an ANOVA, say, the interaction would be ysed and its significance given. However, I can't work out how I can check the interaction between the variables having had to use non-parametric tests. Is there a way I should be looking at the differences between the variables, for instance, using those differences as new variables and running tests on those to see if the differences are significant? I suspect, given my small samples, that these interactions won't be significant, however for my thesis (PhD) it would be useful to discuss these interactions and to have an idea of their effect sizes too, so I do need to run a statistical ysis if I can. I am probably being very dense about this - and I thank you for any help you can offer.