Production of two J/psi mesons in proton-proton collisions at the LHC

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.