The paper is concerned with the question of describing derivations of the algebra \(L(M)\) of all operators affiliated with a commutative von Neumann algebra \(M\). It is shown that there exists a nonzero derivation on \(L(M)\) if and only if the Boolean algebra of all projections in \(M\) is not atomic. In fact, the authors are able to deal with a general class of commutative algebras containing \(L(M)\) as a special case.