  We perform simulations of (3-colour) QCD with 2 quark flavours at a finite
chemical potential $\mu_I$ for isospin($I_3$), and of 2-colour QCD at a finite
chemical potential $\mu$ for quark number. At zero temperature, QCD at finite
$\mu_I$ has a mean-field phase transition at $\mu_I=m_\pi$ to a superfluid
state with a charged pion condensate which spontaneously breaks $I_3$. We study
the finite temperature transition as a function of $\mu_I$. For $\mu_I <
m_\pi$, where this is closely related to the transition at finite $\mu$, this
appears to be a crossover independent of quark mass, with no sign of the
proposed critical endpoint. For $\mu_I > m_\pi$ this becomes a true phase
transition where the pion condensate evaporates. For $\mu_I$ just above $m_\pi$
the transition seems to be second order, while for larger $\mu_I$ it appears to
become first order. At zero temperature, 2-colour QCD also possesses a
superfluid state with a diquark condensate. We study its spectrum of Goldstone
and pseudo-Goldstone bosons associated with chiral and quark-number symmetry
breaking.
