  Vector mesons are copiously produced in ultra-peripheral collisions. In these
collisions, the impact parameter is larger than the sum of the radii of two
projectiles, implying that electromagnetic processes become dominant. The cross
section for this process is sensitive to the gluon distribution and can
therefore probe nuclear gluon shadowing (Pb-Pb) and the gluon structure
function in the nucleon (p-Pb). The ALICE Collaboration has performed the first
measurement of the coherent J/$\psi$ and $\psi$(2S) photoproduction cross
section in Pb-Pb collisions and that for exclusive J/$\psi$ photoproduction off
protons in ultra-peripheral proton-lead collisions at the LHC. The results are
compared to STARLIGHT and to QCD based models.
