  The spectrum of Hamiltonian (Markov matrix) of a multi-species asymmetric
simple exclusion process on a ring is studied. The dynamical exponent
concerning the relaxation time is found to coincide with the one-species case.
It implies that the system belongs to the Kardar-Parisi-Zhang or
Edwards-Wilkinson universality classes depending on whether the hopping rate is
asymmetric or symmetric, respectively. Our derivation exploits a poset
structure of the particle sectors, leading to a new spectral duality and
inclusion relations. The Bethe ansatz integrability is also demonstrated.
