We report on the inclusive J/ψ nuclear modification factor in p-Pb collisions at √ s NN = 5.02 TeV as a function of rapidity y and transverse momentum p T . The experimental coverage extends down to p T = 0 GeV/c in the three rapidity ranges accessible by ALICE (−4.46 < y cms < −2.96, −1.37 < y cms < 0.46, 2.03 < y cms < 3.53). The obtained results as a function of rapidity are in agreement with theory predictions based only on shadowing or on coherent energy loss. At forward and backward rapidity, the ψ(2S) measurement complements the J/ψ results. The ratio between the ψ(2S) and J/ψ cross section is significantly smaller in p-Pb than in pp collisions in both rapidity regions.The seminal paper from T. Matsui and H. Satz [1] published in 1986 initiated intense theoretical and experimental studies of J/ψ production as a probe of deconfinement in nucleus-nucleus (AA) collisions. At LHC energies, in addition to the originally proposed J/ψ suppression due to colour screening, the production of J/ψ due to (re-)combination of charm quarks is suggested as an additional mechanism in two theoretical approaches: the statistical hadronisation at the confinement phase boundary [2,3] and transport models [4,5,6]. The latter assume destruction and production of charmonium states predominantly during the deconfined stage of the system evolution in addition to the primordial production. In this context, the investigation of charmonia in p-Pb collisions at the LHC represents a crucial ingredient for the interpretation of J/ψ AA-measurements. It gives access to nuclear effects, which are not attributable to deconfinement, but can alter the nuclear modification factor R AA = N J/ψ,AA /(< T AA > ·σ J/ψ,pp ). N J/ψ,AA represents in this formula the efficiency corrrected J/ψ-yield per event in AA collisions, T AA denotes the nuclear overlap function and σ J/ψ,pp the J/ψ cross section in proton-proton (pp) collisions at the same centre of mass energy per nucleon-nucleon collision.ALICE has measured J/ψ in p-Pb collisions at a centre of mass energy of 5.02 TeV in the central barrel detectors with a pseudorapidity acceptance |η lab,track | < 0.9 via the dielectron decay channel and in the forward spectrometer with an acceptance of 2.5 < η lab,muon < 4.0 via the dimuon decay channel. A description of the experiment can be found in [7]. An inversion of the beam direction has enabled the muon spectrometer to measure the J/ψ on the proton and on the lead fragmentation side in the asymmetric p-Pb collision system. In the following, the rapidity of the incoming proton is chosen to be positive, which fixes the rapidity sign convention of the dimuon pair. The centre of mass system of the two colliding projectiles is boosted with respect to the laboratory frame system by ∆y = 0.465 resulting in slightly asymmetric rapidity coverages with respect to y = 0: −4.46 < y cms < −2.96 at backward, −1.37 < y cms < 0.43 at central rapidity and 2.03 < y cms < 3.53 at forward rapidity. In the dimuon acceptance, the J/ψ production was measured in six ...