  We argue that in general renormalizable field theories the topological angles
may develop an additive beta function starting no earlier than 2-loop order.
The leading expression is uniquely determined by a single model-independent
coefficient. The associated divergent diagrams are identified and a few
independent methods for extracting the beta function in dimensional
regularization are discussed. We show that the peculiar nature of the
topological angles implies non-trivial constraints on the anomalous dimension
of the CP-violating operators and discuss how a non-vanishing beta function
affects the Weyl consistency conditions. Some phenomenological considerations
are presented.
