Spacetimes admitting a universal redshift function

The conditions are given for a velocity congruence in a Riemannian spacetime admitting a universal redshift function R . This function allows to calculate in a simple way (as a quotient of R values taken at the emission and registration event) the redshift or blueshift connected with an emitter and observer both following the congruence. Spacetimes and congruences with an universal redshift function are shortly discussed.