  We present a study of the two species totally asymmetric diffusion model
using the Bethe ansatz. The Hamiltonian has $U_q(SU(3))$ symmetry. We derive
the nested Bethe ansatz equations and obtain the dynamical critical exponent
from the finite-size scaling properties of the eigenvalue with the smallest
real part. The dynamical critical exponent is 3/2 which is the exponent
corresponding to KPZ growth in the single species asymmetric diffusion model.
