  We discuss inclusive production of pairs of $J/\psi$ quarkonia. Both
leading-order single parton (box) contribution and double-parton contributions
are included. In addition we discuss a contribution of higher-order two-gluon
exchange and a feed down from double $\chi_c$ production. The second two
contributions are important for large rapidity distance between the two
$J/\psi$ mesons and for relatively large cut-offs on quarkonia transverse
momenta. A relation to current experiments is discussed.
