  In 1997, X. Xu \cite{Xiaoping Xu Poisson} invented a concept of
Novikov-Poisson algebras (we call them Gelfand-Dorfman-Novikov-Poisson
(GDN-Poisson) algebras). We construct a linear basis of a free GDN-Poisson
algebra. We define a notion of a special GDN-Poisson admissible algebra, based
on X. Xu's definition and an S.I. Gelfand's observation (see \cite{Gelfand}).
It is a differential algebra with two commutative associative products and some
extra identities. We prove that any GDN-Poisson algebra is embeddable into its
universal enveloping special GDN-Poisson admissible algebra. Also we prove that
any GDN-Poisson algebra with the identity $x\circ(y\cdot z)=(x\circ y )\cdot z
+(x\circ z) \cdot y$ is isomorphic to a commutative associative differential
algebra.
