We discuss a class of models, not based on the Peccei-Quinn mechanism, that solve the strong $\mathrm{CP}$ problem. These are a generalization of a model of Nelson. Improved conditions are given for such models. These conditions are natural and in many simple models are automatically satisfied.

• Received 22 June 1984

DOI:https://doi.org/10.1103/PhysRevD.30.1805