  We define a strong homotopy derivation of (cohomological) degree k of a
strong homotopy algebra over an operad P. This involves resolving the operad
obtained from P by adding a generator with "derivation relations". For a wide
class of Koszul operads P, in particular Ass and Lie, we describe the strong
homotopy derivations by coderivations and show that they are closed under the
Lie bracket. We show that symmetrization of a strong homotopy derivation of an
A-infinity algebra yields a strong homotopy derivation of the symmetrized
L-infinity algebra. We give examples of strong homotopy derivations
generalizing inner derivations.
