We have generalized the methods developed recently by Groeneveld and Penrose for a one‐component system to obtain a lower bound on the domain of convergence of the Mayer fugacity expansion of the pressure,
is the fugacity of the αth component, α=1,•••, ω. This series is convergent for
and where the interaction potential ϕαβ
) of a pair of particles of Species α and β satisfies
for all α, x,
[For a positive interparticle potential, ϕαβ
)≥0, Φ=0.] Consequently the system remains in a single phase in this region. We have also generalized the inequalities of Lieb, Penrose, Lebowitz, and Percus to this case. For positive potentials upper (lower) bounds are gotten for the pressure and the distribution functions by expanding in a Taylor series up to terms of even (odd) total order in the fugacities.