  We formulate the low energy limit of QCD like partition functions with
bosonic quarks at nonzero chemical potential. The partition functions are
evaluated in the parameter domain that is dominated by the zero momentum modes
of the Goldstone fields. We find that partition functions with bosonic quarks
differ structurally from partition functions with fermionic quarks. Contrary to
the theory with one fermionic flavor, where the partition function in this
domain does not depend on the chemical potential, a phase transition takes
place in the theory with one bosonic flavor when the chemical potential is
equal to $m_\pi/2$. For a pair of conjugate bosonic flavors the partition
function shows no phase transition, whereas the fermionic counterpart has a
phase transition at $\mu = m_\pi/2$. The difference between the bosonic
theories and the fermionic ones originates from the convergence requirements of
bosonic integrals resulting in a noncompact Goldstone manifold and a covariant
derivative with the commutator replaced by an anti-commutator.
