The Bellman–Harris branching process is more general than the processes considered in the preceding chapters. Lifetimes of particles are nonnegative random variables with arbitrary distributions. It is described as follows. A single ancestor particle is born at t = 0. It lives for time τ which is a random variable with cumulative distribution function (Formula Presented). At the moment of death, the particle produces a random number of progeny according to a probability distribution with pgf f(s). Each of the first generation progeny behaves, independently of each other and the ancestor, as the ancestor particle did, i.e., it lives for a random time distributed according to (Formula Presented) and produces a random number of progeny according to f(s). If we denote Z(t) the particle count at time t, we obtain a stochastic process (Formula Presented). This so-called age-dependent process is generally non-Markov, but two of its special cases are Markov: the Galton–Watson process and the age-dependent branching process with exponential lifetimes. The Bellman–Harris process is more difficult to analyze, but it has many properties similar to these two processes.