  This paper deals with the variety of commutative nonassociative algebras
satisfying the identity $L_x^3+ \gamma L_{x^3} = 0$, $\gamma \in K$. Correa et
al proved that if $\gamma = 0,1$ then any such finitely generated algebra is
nilpotent. Here we generalize this result by proving that if $\gamma \neq -1$,
then any such algebra is locally nilpotent. Our results require characteristic
$\neq 2,3$.
