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 equival
ent. We transport a part of Morita theory to the operadic context by studyi
ng modules over operads. As an application of this philosophy, we consider
an operadic version of the sheaf of linear differential operators on a (sup
er)manifold M and give a comparison theorem between algebras over this shea
f on M and M-red.