  Universal enveloping commutative Rota-Baxter algebras of pre- and
postcommutative algebras are constructed. We prove that the pair of varieties
(commutative Rota-Baxter algebras of nonzero weight,postcommutative algebras)
is a PBW-pair and the pair (commutative Rota-Baxter algebras of zero
weight,precommutative algebras) is not.
