A stochastic population model is constructed based on assumptions similar to those made by P.H. Lealie in his deterministic theory. For this stochastic model a linear matrix recurrence relation is derived which determinea precisely the first two moments of the age group random variables at each integral point of time. Several results about the asymptotic bebviour of the population are mentioned. These results are not new, since they me derived for a process which may be regarded as a special case of the multi-type Galton-Watson process, but they appear in a new form which is generalized to include the higher-order moments of all multi-type Galton-Watson branching processes. The matrix recurrence relation has a form which is convenient for analysing more sophisticated models, and some examples are mentioned.