You want to analyze a parameter with a non-parametric method?

GLMs are parametric. Binomial hat a probability parameter, Poisson a rate parameter, Gamma has a shape and a rate parameter, and Normal has a location and a variance parameter.

As Jochen says, it is not clear what you are wanting. Do you mean procedures that do not assume a particular distribution for the residuals, not assume the normal, or something else?

If you want to analyze group differences regarding a non-normally distributed dependent metric variable including possible covariates and normalization of the dependent variable (e.g., by a logarithmic transformation) is not possible using a generalized linear model for rank-scaled variables would be a good option.     

 Thanks for the rapid help! I forgot log transformation, that will do.

Using a normal (G)LM with a log-transformed response means to analyze differences in the logs, that is, log-ratios. If this is what you want you may consider a Gamma GLM using a log-link. If you are really interested in analyzing differences, then a Gamma GLM with identity link should do.