We consider a system of Markov processes of finitely-many particles wh
ich exchange their energies in pairs at random times. A law of large n
umbers for this system means that the empirical measures of the proces
ses may be approximated (as the number of particles increases) by the
solution of a nonlinear evolution equation (the so-called McKean-Vlaso
v limit). This work presents two results of this type. The first one c
oncerns the empirical processes and gives a probabilistic method for s
olving the nonlinear equation. The second is stated in the path scheme
and extends classical results of chaos propagation by Kac (1956) and
McKean (1967).