Elementary distributions such as the Poisson, the Logarithmic and the Binomial which can be formulated on the basis of simple models have been found to be inadequate to describe the situations which occur in a number of phenomena. The Neyman Type A (cf. Evans [5]), the Negative Binomial (cf. Bliss and Fisher [3]), and the Poisson Binomial (cf. McGuire et al. [8]), which combine two of the elementary distributions through the processes of compounding and generalizing (cf. Gurland [7]), have been fitted with varying degrees of success to data from a number of biological populations. The aim of this paper is to study what may be called the Poisson Pascal distribution which includes the Neyman Type A and Negative Binomial as particular limiting cases and serves as a natural complement of the Poisson Binomial.