The Leslie matrix model (Leslie, 1945) for discrete population growth has been modified and used several times in population dynamics. A review is given of the basic model (nt+ 1 = Ant) and of its principal modifications. The modifications relating to the influences of 'internal' or 'external' factors to the population are studied with greater detail. The same applies to models where the population is divided in stages rather than in age classes.In the same line, Hadjibiros (1975Hadjibiros ( , 1976) studied a more general model, where the transition matrix corresponds to a population divided in stages of unequal duration, and where the time varying influences of the 'internal' or ~external' factors are included. This model offers the possibility of computer simulation of the population dynamics of a natural population represented by a demographic vector.Some kind of relationship is proposed between the general matrix model and the Lefkovitch matrix (Lefkovitch, 1964(Lefkovitch, , 1965; the elements of which, obtained by regression techniques from census data, describe the biological dependance of a stage i at time t + 1 on a stage j at time t.