The Bird and Nanbu systems are particle systems used to approximate the
solution of the mollied Boltzmann equation. In particular, they have the
propagation of chaos property. Following [GM94, GM97, GM99], we use coupling
techniques and results on branching processes to write an expansion of the
error in the propagation of chaos in terms of the number of particles, for
slightly more general systems than the ones cited above. This result leads to
the proof of the a.s convergence and the centrallimit theorem for these
systems. In particular, we have a central-limit theorem for the empirical
measure of the system under less assumptions then in [M{\'e}l98]. As in [GM94,
GM97, GM99], these results apply to the trajectories of particles on an
interval [0; T]
