A discussion of a multitype branching process for discrete time which is a birth and death process determined by the random variables describing the first generation. The process is critical if the expectation matrix for one generation has its maximum real eigenvalue equal to 1. With probability 1, such a process dies after a finite number of generations. This paper investigates the population size of the nth generation of such a process given that the nth generation is not empty. The results of previous investigations are extended by showing that a certain conditional random variable has a limiting distribution of exponential type. This follows from results about the iterates of a k-dimensional analytic mapping near a fixed point.
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