  In this paper we study the Lie algebras of derivations of two-step nilpotent
algebras. We obtain a class of Lie algebras with trivial center and abelian
ideal of inner derivations. Among these, the relations between the complex and
the real case of the indecomposable Heisenberg Leibniz algebras are thoroughly
described. Finally we show that every almost inner derivation of a complex
nilpotent Leibniz algebra with one-dimensional commutator ideal, with three
exceptions, is an inner derivation.
