  Associative rings A, B are called Morita equivalent when the categories of
left modules over them are equivalent. We call two classical linear operads P,
Q Morita equivalent if the categories of algebras over them are equivalent. We
transport a part of Morita theory to the operadic context by studying modules
over operads. As an application of this philosophy, we consider an operadic
version of the sheaf of linear differential operators ona a (super) manifold M
and give a comparison theorem between algebras over this sheaf on M and
M_{red}. The paper is dedicated to A.N.Tyurin on the occasion of his 60th
birthday.
