Constraints imposed byCPconservation in the presence of pseudoparticles

We elaborate on an earlier discussion of CP conservation of strong interactions which includes the effect of pseudoparticles. We discuss what happens in theories of the quantum-chromodynamics type when we include weak and electromagnetic interactions. We find that strong CP conservation remains a natural symmetry if the full Lagrangian possesses a chiral U (1) invariance. We illustrate our results by considering in detail a recent model of (weak) CP nonconservation.