  Different types of superfluid ground states have been investigated in systems
of two species of fermions with Fermi surfaces that do not match. This study is
relevant for cold atomic systems, condensed matter physics and quark matter. In
this paper we consider this problem in the case the fermionic quasi-particles
can transmute into one another and only their total number is conserved. We use
a BCS approximation to study superconductivity in two-band metallic systems
with inter and intra-band interactions. Tuning the hybridization between the
bands varies the mismatch of the Fermi surfaces and produces different
instabilities. For inter-band attractive interactions we find a first order
normal-superconductor and a homogeneous metastable phase with gapless
excitations. In the case of intra-band interactions, the transition from the
superconductor to the normal state as hybridization increases is continuous and
associated with a quantum critical point. The case when both interactions are
present is also considered.
