  We consider the question of vacuum alignment in the recently proposed
"composite technicolor" (CTC) models. In order for these models to work, an
"ultrafermion" condensate must align in a particular way, driven by the
competition between ultrafermion masses and "flavor" gauge boson exchange. We
show that for ultrafermion masses large enough to explain the top quark mass,
order-of-magnitude estimates are sufficient to establish that the required
vacuum alignment cannot occur for perturbative values of the flavor gauge
couplings. If the top quark gets its mass from some other mechanism, a detailed
calculation is required. Using spectral function sum rules and a vector-meson
saturation approximation which is known to work well in QCD, we determine the
correct vacuum for this case in a limit where the flavor gauge bosons are
weakly coupled and the number of ultracolors $N$ is large. We again find that
the vacuum required by CTC models does not occur for perturbative values of the
flavor gauge couplings. We conclude that there is no evidence that the vacuum
aligns as required in CTC models.
