  The breaking of conventional linear k_\perp-factorization for hard processes
in a nuclear environment is by now well established. Here we report a detailed
derivation of the nonlinear k_\perp-factorization relations for the production
of quark-gluon dijets. This process is of direct relevance to dijets in the
proton hemisphere of proton-nucleus collisions at energies of the Relativistic
Heavy Ion Collider (RHIC). The major technical problem is a consistent
description of the non-Abelian intranuclear evolution of multiparton systems of
color dipoles. Following the technique developed in our early work [ N.N.
Nikolaev, W. Sch\"afer, B.G. Zakharov and V.R. Zoller, J. Exp. Theor. Phys.\
{\bf 97} (2003) 441], we reduce the description of the intranuclear evolution
of the $qgg\bar{q}$ state to the system of three coupled-channel equations in
the space of color singlet 4-parton states $\ket{3\bar{3}}, \ket{6\bar{6}}$ and
$\ket{15\bar{15}}$ (and their large-N_c generalizations). At large number of
colors N_c, the eigenstate $(\ket{6\bar{6}}-\ket{15\bar{15}})/\sqrt{2}$
decouples from the initial state $\ket{3\bar{3}}$. The resulting nuclear
distortions of the dijet spectrum exhibit much similarity to those found
earlier for forward dijets in Deep Inelastic Scattering (DIS). Still there are
certain distinctions regarding the contribution from color-triplet $qg$ final
states and from coherent diffraction excitation of dijets. To the large-N_c
approximation, we identify four universality classes of nonlinear
k_\perp-factorization for hard dijet production.
