This paper deals with an age-structured epidemic model with a non-separable transmission coefficient. We deal with a model where the population is divided into classes containing susceptible, infected and immune individuals suitable for most common childhood diseases. We show how the same threshold and stability results can be obtained as for the case when the transmission coefficient is separable. There is a threshold condition which can be expressed in terms of the spectral radius of a certain operator. The existence and stability of the possible equilibria are examined in terms of this threshold condition. The results are extended to take into account the effect of a latent period and the fact that new-born individuals are protected by maternal antibodies.