  The double quarkonium production in single and double diffractive processes
is investigated considering $pp$ collisions at the Run 2 LHC energy. Using the
nonrelativistic QCD (NRQCD) factorization formalism for the quarkonium
production and the Resolved Pomeron model to describe the diffractive
processes, we estimate the rapidity and transverse momentum dependencies of the
cross sections for the $J/\Psi J/\Psi$ and $\Upsilon \Upsilon$ production. 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 double
quarkonium production in diffractive processes is not negligible and that its
study can be useful to test the underlying assumptions present in the
description of the single and double diffractive processes.
