We consider cocycles over minimal compact systems which take values in a locally compact, non-abelian group $G$ and investigate their dynamics. The case of nilpotent groups $G$ behaves not much different from the abelian case: if the base transformation is an isometry, we can exclude `irregular' behaviour of cocycles (this is a joint work with Gernot Greschonig). Considering solvable groups $G$ the situation becomes more difficult and the issue of regularity is only partly solved in some special cases.