  We analyze the ultraviolet to infrared evolution and nonperturbative
properties of asymptotically free ${\rm SU}(N) \otimes {\rm SU}(N-4) \otimes
{\rm U}(1)$ chiral gauge theories with $N_f$ copies of chiral fermions
transforming according to $([2]_N,1)_{N-4} + ([\bar 1]_N,[\bar
1]_{N-4})_{-(N-2)} + (1,(2)_{N-4})_N$, where $[k]_N$ and $(k)_N$ denote the
antisymmetric and symmetric rank-$k$ tensor representations of SU($N$) and the
rightmost subscript is the U(1) charge. We give a detailed discussion for the
lowest nondegenerate case, $N=6$. These theories can exhibit both self-breaking
of a strongly coupled gauge symmetry and induced dynamical breaking of a weakly
coupled gauge interaction symmetry due to fermion condensates produced by a
strongly coupled gauge interaction. A connection with the dynamical breaking of
${\rm SU}(2)_L \otimes {\rm U}(1)_Y$ electroweak gauge symmetry by the quark
condensates $\langle \bar q q\rangle$ due to color SU(3)$_c$ interactions is
discussed. We also remark on direct-product chiral gauge theories with fermions
in higher-rank tensor representations.
