  We use 2-color QCD as a model to study the effects of simultaneous presence
of chemical potentials for isospin charge, $\mu_I$, and for baryon number,
$\mu_B$. We determine the phase diagrams for 2 and 4 flavor theories using the
method of effective chiral Lagrangians at low densities and weak coupling
perturbation theory at high densities. We determine the values of various
condensates and densities as well as the spectrum of excitations as functions
of $\mu_I$ and $\mu_B$. A similar analysis of QCD with quarks in the adjoint
representation is also presented. Our results can be of relevance for lattice
simulations of these theories. We predict a phase of inhomogeneous condensation
(Fulde-Ferrel-Larkin-Ovchinnikov phase) in the 2 colour 2 flavor theory, while
we do not expect it the 4 flavor case or in other realizations of QCD with a
positive measure.
