  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.
