In this paper, we investigate the derivations in evolution algebras that are power-associative. This problem is reduced to that of power-associative evolution nilalgebras. We show how to calculate derivations in decomposable algebras. This calculation shows that it is enough to describe derivations in indecomposable evolution algebras. We first determine the derivation algebra of n-dimensional indecomposable associative evolution nilalgebras with one-dimensional annihilator. We describe the derivation algebra of indecomposable nilalgebras, up to dimension 6, that are associative or not. In each case, we give the ideal of inner derivations.

evolution algebra, derivation, inner derivation, power associativity, nilalgebra.