  In this paper, we consider Lie-admissible algebras, which are free Novikov
and free Lie-admissible algebras with an additional metabelian identity. We
construct a linear basis for both free metabelian Novikov and free metabelian
Lie-admissible algebras. Additionally, we describe a space of symmetric
polynomials for both the free metabelian Novikov algebra and the free
metabelian Lie-admissible algebra.
