  We investigate some properties of the nonequilibrium stationary state (NESS)
of a one dimensional open system consisting of first and second class (type 1
and type 2) particles. The dynamics are totally asymmetric but the rates for
the different permitted exchanges (10 -> 01, 12 -> 21, and 20 -> 02) need not
be equal. The entrance and exit rates of the different species can also be
different. We show that for certain classes of rates one can compute the
currents and phase diagram, or at least obtain some monotonicity properties.
For other classes one can obtain a matrix representation of the NESS; this
generalizes previous work in which second class particles can neither enter nor
leave the system. We analyze a simple example of this type and establish the
existence of a randomly located shock at which the typical density profiles of
all three species are discontinuous.
