Simple deterministic mathematical models for the spread of common childhood diseases are considered. The population is divided into compartments containing susceptible, infectious and immune individuals. The spread of the disease is modelled by a set of differential equations which describe the transfer of individuals between these classes. Some equilibrium and stability results are described and numerical investigations presented which support the analytical results. In these numerical investigations we pay particular attention to whether the level of disease will damp down to a steady equilibrium value and to various methods of predicting the periods of disease cycles.