The development of a population model in which population state is defined by a matrix of numbers at age and length is described. Functional forms for processes that fitted Hauraki Gulf–Bay of Plenty (New Zealand) snapper (Pagrus auratus) population data were developed. The model was fitted to: commercial and research samples of proportions at age and length, commercial samples of proportions at age, tag–recapture estimates of numbers at length, a catch per unit effort abundance index, and sea surface temperature data. For each age–length element of the state matrix, the model determines a transition vector that gives a distribution of non-negative growth increments. Mean growth is both length- and age–length-dependent, but also varies between years. Annual mean growth and annual year-class strength were both found to be positively related to sea surface temperature, but during different seasons. It was also found that variations in growth between years resulted in moderate and sustained fluctuations in population biomass. Diagnostic tools that were helpful in fitting the age–length data are described, and potentially fruitful model developments are suggested.