ALICE has measured quarkonium production in p-Pb collisions at backward (-4.46 < y(cms) < 2.96), mid (-1.37 < y(cms) < 0.43) and forward (2.03 < y(cms) < 3,53) rapidity (y) regions down to zero transverse momentum (p(T)). The inclusive J/psi production has been studied at mid-y in p-Pb interactions at root S-NN =3D 5.02 TeV and at forward and backward y in p-Pb collisions at root S-NN =3D 5.02 TeV and 8.16 TeV. The comparison of the J/psi production to the one of the loosely bound psi(2S) state is discussed, together with new results on the nuclear modification factors of the gamma(1S) and gamma(2S) states measured at forward and backward y. All the results will be compared to those obtained at lower energies and with available theoretical calculations.
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