  In this paper, we study Novikov algebras satisfying nontrivial identities. We
show that a Novikov algebra over a field of zero characteristic that satisfies
a nontrivial identity satisfies some unexpected "universal" identities, in
particular, right associator nilpotence, and right nilpotence of the commutator
ideal. This, in particular, implies that a Novikov algebra over a field of zero
characteristic satisfies a nontrivial identity if and only if it is
Lie-solvable. We also establish that any system of identities of Novikov
algebras over a field of zero characteristic follows from finitely many of
them, and that the same holds over any field for multilinear Novikov
identities. Some analogous simpler statements are also proved for commutative
differential algebras.
