  We study QCD-like theories with pseudoreal fermions at finite baryon density.
Such theories include two-color QCD with quarks in the fundamental
representation of the color group as well as any-color QCD with quarks in the
adjoint color representation. In all such theories the lightest baryons are
diquarks. At zero chemical potential $\mu$ they are, together with the
pseudoscalar mesons, the Goldstone modes of a spontaneously broken enlarged
chiral symmetry group. Using symmetry principles, we derive the low-energy
effective Lagrangian for these particles. We find that a second order phase
transition occurs at a value of $\mu$ equal to half the mass of the Goldstone
modes. For values of $\mu$ beyond this point the scalar diquarks Bose condense
and the diquark condensate is nonzero. We calculate the dependence of the
chiral condensate, the diquark condensate, the baryon charge density, and the
masses of the diquark and pseudoscalar excitations on $\mu$ at finite bare
quark mass and scalar diquark source. The relevance of our results to lattice
QCD calculations and to real three-color QCD at finite baryon density is
discussed.
