  We consider central exclusive production of $gg$ dijets in proton-proton
(proton-antiproton) collisions at LHC and Tevatron for different intermediate
and final gluon polarisations. The amplitude for the process is derived within
the $k_\perp$-factorization approach (with both the standard QCD and the
Lipatov's effective three-gluon verticies) and is considered in various
kinematical asymptotia, in particular, in the important limit of high-$p_\perp$
jets. Compared to earlier works we include emissions of gluons from different
gluonic $t$-channel lines as well as emission of quark-antiquark dijets.
Rapidity distributions, gluon jet $p_\perp$ distributions and invariant dijet
mass distributions are presented. We explore the competition of the standard
diagram with both jets emitted from a single $t$-channel gluon and the one with
the emission from both $t$-channel gluons. The second mechanism requires a
special treatment. We propose two different approaches. Including special
kinematics and using properties of off-diagonal gluons at small $x$ and $\xi$
we arrive to correlations in two-dimensional distributions in rapidity of one
and second jet. We find that the second contribution is much smaller than that
known from the literature. The digluon production constitutes an important
background to exclusive Higgs production.
