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Are Nonrenormalizable Gauge Theories Renormalizable?

We raise the issue whether gauge theories, that are not renormalizable in the usual power-counting sense, are nevertheless renormalizable in the modern sense that all divergences can be cancelled by renormalization of the infinite number of terms in the bare action. We find that a theory is renormalizable in this sense if the {\em a priori} constraints that we impose on the form of the bare action correspond to the cohomology of the BRST transformations generated by the action. Recent cohomology theorems of Barnich, Brandt, and Henneaux are used to show that conventionally nonrenormalizable theories of Yang-Mills fields (such as quantum chromodynamics with heavy quarks integrated out) and/or gravitation are renormalizable in the modern sense.