Varieties of two-step solvable algebras of type $(\gamma,\delta)$

The structure of the set of all nonnilpotent subvarieties of the variety of two-step solvable algebras of type $(\gamma,\delta)$ is studied. An additive basis of a free metabelian $(\gamma,\delta)$-algebra is constructed. It is proved that any identity in a nonnilpotent metabelian $(\gamma,\delta)$-algebra of degree at least 6 is a consequence of four defining relations.