  We have investigated the phase behaviour of a symmetrical binary fluid
mixture for the situation where the chemical potentials $\mu_1$ and $\mu_2$ of
the two species differ. Attention is focused on the set of interparticle
interaction strengths for which, when $\mu_1=\mu_2$, the phase diagram exhibits
both a liquid-vapor critical point and a tricritical point. The corresponding
phase behaviour for the case $\mu_1\ne\mu_2$ is investigated via
integral-equation theory calculations within the mean spherical approximation
(MSA), and grand canonical Monte Carlo (GCMC) simulations. We find that two
possible subtypes of phase behaviour can occur, these being distinguished by
the relationship between the critical lines in the full phase diagram in the
space of temperature, density, and concentration. We present the detailed form
of the phase diagram for both subtypes and compare with the results from GCMC
simulations, finding good overall agreement. The scenario via which one subtype
evolves into the other, is also studied, revealing interesting features.
