A simple two-species asymmetric exclusion model is introduced. It cons
ists of two types of oppositely charged particles driven by an electri
c field and hopping on an open chain. The phase diagram of the model i
s calculated in the mean-field approximation and by Monte Carlo simula
tions. Exact solutions are given for special values of the parameters
defining its dynamics. The model is found to exhibit two phases in whi
ch spontaneous symmetry breaking takes place, where the two currents o
f the two species are not equal.