Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but they are structurally unable to describe stochastic fluctuations or system-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using e.g., the Bellman-Harris equation, cannot resolve a population's age-structure and are unable to quantify population-size dependencies. In this talk, I will present a systematic derivation of a new fully stochastic kinetic theory for interacting age-structured particles. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an ageing population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a BBGKY-like hierarchy. However, explicit solutions are derived in two simple limits and compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and system-size-dependent stochastic dynamics