  The ALICE Collaboration has studied the inclusive $\psi(\rm 2S)$ production
in p-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV at the CERN LHC.
Measurements are performed, in the $\mu^{+}\mu^{-}$ decay channel, in a forward
(2.03$<y_{\rm cms}<$3.53) and in a backward (-4.46$<y_{\rm cms}<$-2.96) centre
of mass rapidity ranges, as a function of transverse momentum or event
activity. The $\psi(\rm 2S)$ production is compared to the $\rm J/\psi$ one
through the double ratio $[\sigma_{\psi(\rm 2S)}/\sigma_{\rm J/\psi}]_{\rm
pPb}/[\sigma_{\psi(\rm 2S)}/\sigma_{\rm J/\psi}]_{\rm pp}$ between the cross
sections evaluated in p-Pb and pp collisions and by calculating the $\rm
J/\psi$ and $\psi(\rm 2S)$ nuclear modification factors. Results indicate that
the $\psi(\rm 2S)$ production is suppressed with respect to pp and, in
particular in the backward rapidity region, the suppression is stronger than
the $\rm J/\psi$ one. This unexpected difference between the $\rm J/\psi$ and
$\psi(\rm 2S)$ behaviour, not accounted for by theoretical models based on
nuclear parton shadowing and coherent energy loss mechanisms, indicates the
presence of sizeable final state effects on the $\psi(\rm 2S)$ production.
