  We focus on the problem of disentangling the single (SPS) and double (DPS)
parton scattering modes in the production of \J pairs at the LHC conditions.
Our analysis is based on comparing the shapes of the differential cross
sections and on studying their behavior under imposing kinematical cuts. On the
SPS side, we consider the leading-order ${\cal O}(\alpha_s^4)$ contribution
with radiative corrections (taken into account in the framework of the \ktf
approach) and the subleading ${\cal O}(\alpha_s^6)$ contribution from \pd
~gluon-gluon scattering represented by one gluon exchange and two gluon
exchange mechanisms. We come to the conclusion that disentangling the SPS and
DPS modes is rather difficult on the basis of azimuthal correlations, while the
rapidity difference looks more promising, provided the acceptance of the
experimental detectors has enough rapidity range.
