  In the asymmetric simple exclusion process on the integers each particle
waits exponential time, then with probability p it moves one step to the right
if the site is unoccupied, otherwise it stays put; and with probability q=1-p
it moves one step to the left if the site is unoccupied, otherwise it stays
put. In previous work the authors, using the Bethe Ansatz, found for N-particle
ASEP a formula --- a sum of multiple integrals --- for the probability that a
system is in a particular configuration at time t given an initial
configuration. The present work extends this to the case where particles are of
different species, with particles of a higher species having priority over
those of a lower species. Here the integrands in the multiple integrals are
defined by a system of relations whose consistency requires verifying that the
Yang-Baxter equations are satisfied.
