  This paper develops the basic analytical theory related to some recently
introduced crowd dynamics models. Where well posedness was known only locally
in time, it is here extended to all of $\reali^+$. The results on the stability
with respect to the equations are improved. Moreover, here the case of several
populations is considered, obtaining the well posedness of systems of multi-D
non-local conservation laws. The basic analytical tools are provided by the
classical Kruzkov theory of scalar conservation laws in several space
dimensions.
