Conformal vector fields and conformal-type collineations in space-times

Some restrictions on the existence of homothetic and conformal vector field s in space-times which already admit some Killing symmetry are established, In particular, the behaviour of Weyl invariants and the nature of the Petr ov type of the Weyl tensor along the integral curves of conformal vector fi elds are studied. This results in important restrictions between conformal vector fields and Killing orbits. A brief remark is made on Weyl collineati ons.