  The general theory developed by Ben Yaacov for metric structures provides
Fra\"iss\'e limits which are approximately ultrahomogeneous. We show here that
this result can be strengthened in the case of relational metric structures. We
give an extra condition that guarantees exact ultrahomogenous limits. The
condition is quite general. We apply it to stochastic processes, the class of
diversities, and its subclass of $L_1$ diversities.
