Here we present recent results of our calculations of χ c pair production, mainly in the single
parton scattering (SPS) mode. An important feature is that the single-gluon exchange mechanism
can to some extent mimic the behaviour of double parton scattering (DPS) production. Off-shell
matrix elements for $g ∗ g ∗ → χ_{cJ_1} χ_{cJ_2}$ were derived and then used in the k T -factorization approach
for the $pp → χ_{cJ_1} χ_{cJ_2}$ reaction. Different combination of the $χ_c$ mesons are considered. A similar
analysis is repeated for the collinear factorization approach, but now including the associated
production with a gluon (jet). The leading order contributions ($2 → 2$ processes) are rather small,
compared to the $k_T$-factorization result. But the addition of $2 → 3$ processes helps to recover the
latter results.