  The local composite gluon-ghost operator $({1/2}A^{a\mu}A_{\mu}^{a}+\alpha
\bar{c}^{a}c^{a})$ is analysed in the framework of the algebraic
renormalization in SU(N) Yang-Mills theories in the Landau, Curci-Ferrari and
maximal abelian gauges. We show, to all orders of perturbation theory, that
this operator is multiplicatively renormalizable. Furthermore, its anomalous
dimension is not an independent parameter of the theory, being given by a
general expression valid in all these gauges. We also verify the relations we
obtain for the operator anomalous dimensions by explicit 3-loop calculations in
the MSbar scheme for the Curci-Ferrari gauge.
