  We extend to binary relational systems the notion of compact and normal
structure, introduced by J.P.Penot for metric spaces, and we prove that for the
involutive and reflexive ones, every commuting family of relational
homomorphisms has a common fixed point. The proof is based upon the clever
argument that J.B.Baillon discovered in order to show that a similar conclusion
holds for bounded hyperconvex metric spaces and then refined by the first
author to metric spaces with a compact and normal structure. Since the
non-expansive mappings are relational homomorphisms, our result includes those
of T.C.Lim, J.B.Baillon and the first author. We show that it extends the
Tarski's fixed point theorem to graphs which are retracts of reflexive oriented
zigzags of bounded length. Doing so, we illustrate the fact that the
consideration of binary relational systems or of generalized metric spaces are
equivalent.
