A discrete-time two-sex stochastic population model is developed. All entities (single males, single females, or couples) are grouped according to their ages, and during a unit time interval, each entity has a choice of several outcomes with fixed conditional probabilities. The model assumes that the number of marriages between men aged x and women aged y is equal to the minimum of the number of men aged x desiring marriage with a woman aged y and the number of women aged y desiring marriage with a man aged x. It follows that if a large excess of males of a11 ages is maintained in the population, the female component grows as a multi-type Galton-Watson process. Under such circumstances, the females have perfect freedom in their choice of marriage partner, and the use of a multi-type Galton-Watson process is very realistic. The same result is true for the male component of the population. Ir there are no males (or females), no marriages take place, so the model is realistic on this score also. A complex computer program is described, and a detailed numerical example given.