  We study a connection between the isochronicity of a center of a polynomial
vector field and the existence of a polynomial commuting system. We demonstrate
an isochronous system of degree 4 which does not commute with any polynomial
system. We prove that among the Newton polynomial systems only the Lienard and
Abel systems may commute with transversal polynomial fields. We give a full and
constructive description of centralizers of the Abel polynomial systems. We
give new examples of isochronous systems.
