Families of quasigroup operations satisfying the generalized distributive law

The previous paper was concerned with systems of equations over a certain family $\mathcal S$ of quasigroups. In that work a method of elimination of an outermost variable from the system of equations was suggested and it was shown that further elimination of variables requires that the family $\mathcal S$ of quasigroups satisfy the generalized distributive law (GDL). In this paper we describe families $\mathcal S$ that satisfy GDL. The results are applied to construct classes of easily solvable systems of equations.