  In this paper we study the inclusive and diffractive double quarkonium
production. Based on the nonrelativistic QCD (NRQCD) factorization formalism
for the quarkonium production mechanism we estimate the rapidity and transverse
momentum dependence of the cross section for the $J/\Psi J/\Psi$ and $\Upsilon
\Upsilon$ production in diffractive processes at LHC energies. The
contributions of the color-singlet and color-octet channels are estimated and
predictions for the total cross sections in the kinematical regions of the LHC
experiments are also presented. Our results demonstrate that the contribution
of diffractive processes is not negligible and that its study can be useful to
test the Resolved Pomeron model.
