  We study the relativistic Vlasov-Maxwell system which describes large systems
of particles interacting by means of their collectively generated forces. If
the speed of light $c$ is considered as a parameter then it is known that in
the Newtonian limit $c\to\infty$ the Vlasov-Poisson system is obtained. In this
paper we determine the next order approximate system, which in the case of
individual particles usually is called the Darwin approximation.
