In the leading order of a modified 1/Nc expansion, we show that a class of gauge-Higgs-Yukawa systems in four dimensions give non-trivial and well-defined theories in the continuum limit. The renormalized Yukawa coupling y and the quartic scalar coupling tl have to lie on a certain line in the (y, tl) plane and the line terminates at an upper bound. The gauged Nambu-Jona-Lasinio (NJL) model in the limit of its ultraviolet cutoff going to infinity, is shown to become equivalent to the gauge-Higgs-Yukawa system with the coupling constants just on that terminating point. This proves the renormalizability of the gauged NJL model in four dimensions. The effective potential for the gauged NJL model is calculated by using renormalization group technique and confirmed to be consistent with the previous result by Kondo, Tanabashi and Yamawaki obtained by the ladder Schwinger-Dyson equation. It is generally a difficult problem whether a theory defined with an ultraviolet cutoff (such as in lattice formulation) really has a well-defined (i.e., finite) continuum limit which is not a free theory. If the theory becomes necessarily free in the continuum limit, the theory is called trivial and if it gives an interacting theory, it is called nontriviaL This triviality or nontriviality is always a problem independently of whether the theory is perturbatively renormalizable or not. But, if a theory is perturbatively non-renormalizable and nevertheless gives a nontrivial continuum limit, people prefer to call it (non-perturbatively) renormalizable rather than simply calling it nontriviaL We also follow this terminology in this paper. We discuss two problems in this paper. One is the triviality problem of a class of gauge-Higgs-Yukawa systems in four dimensions which are of course (pertur batively) renormalizable. We examine and clarify when they can give well-defined, nontrivial theories in the continuum limit (i.e., when the ultraviolet cutoff goes to infinity)_ Another is the renormalizability of gauged Nambu-Jona-Lasinio (NJL) models in four dimensions which are (perturbatively) non-renormalizable. We note that the gauged NJL models are equivalent to special cases of gauge-Higgs-Yukawa systems at the stage with the ultraviolet cutoff kept finite. Considering the limit of the cutoff going to infinity, we can show that, under a certain condition, the gauged NJL models give well-defined continuum limits which are equivalent to specific nontrivial gauge-Higgs-Yukawa theories. Namely, gauged NJL models become renormalizable in the sense of the above terminology_ Kondo, Tanabashi and YamawakPJ (KTY) have studied the gauged NJL model *l Fellow of the Japan Society for the Promotion of Science for Japanese Junior Scientists. Address