  Classical results for exchangeable systems of random variables are extended
to multi-class systems satisfying a natural partial exchangeability assumption.
It is proved that the conditional law of a finite multi-class system, given the
value of the vector of the empirical measures of its classes, corresponds to
independent uniform orderings of the samples within each class, and that a
family of such systems converges in law if and only if the corresponding
empirical measure vectors converge in law. As a corollary, convergence within
each class to an infinite i.i.d. system implies asymptotic independence between
different classes. A result implying the Hewitt-Savage 0-1 Law is also
extended.
