We analyze the ultraviolet to infrared evolution and nonperturbative properties of asymptotically free SU(N)⊗ - SU(N-4)⊗ - U(1) chiral gauge theories with Nf copies of chiral fermions transforming according to (N,1)N-4+([1̄]N,[1̄]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 SU(2)L? - U(1)Y electroweak gauge symmetry by the quark condensates ?q̄q? 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.