  We consider the constraints that critical dynamics places on models with a
top quark condensate or strong extended technicolor (ETC). These models require
that chiral-symmetry-breaking dynamics at a high energy scale plays a
significant role in electroweak symmetry breaking. In order for there to be a
large hierarchy between the scale of the high energy dynamics and the weak
scale, the high energy theory must have a second order chiral phase transition.
If the transition is second order, then close to the transition the theory may
be described in terms of a low-energy effective Lagrangian with composite
``Higgs'' scalars. However, scalar theories in which there are more than one
$\Phi^4$ coupling can have a {\it first order} phase transition instead, due to
the Coleman-Weinberg instability. Therefore, top-condensate or strong ETC
theories in which the composite scalars have more than one $\Phi^4$ coupling
cannot always support a large hierarchy. In particular, if the
Nambu--Jona-Lasinio model solved in the large-$N_c$ limit is a good
approximation to the high-energy dynamics, then these models will not produce
acceptable electroweak symmetry breaking.
