  Based on the research of Rota-Baxter family algebra and Hopf
$\pi$-(co)algebra, we integrate the Rota-Baxter operator into Hopf
$\pi$-(co)algebra, which leads to the concept of Rota-Baxter (Hopf)
$\pi$-(co)algebra. The relations among some related $\pi$-algebraic structures
are discussed, and at the same time concrete examples from the algebras of
dimensions 2,3 and 4 are given.
