The production of Y (1S), Y (2S), and Y (3S) is investigated in pPb and pp collisions at centre-of-mass energies per nucleon pair of 5.02 TeV and 2.76 TeV, respectively. The datasets correspond to integrated luminosities of about 31 nb −1 (pPb) and 5.4 pb −1 (pp), collected in 2013 by the CMS experiment at the LHC. Upsilons that decay into muons are reconstructed within the rapidity interval | y CM | < 1 . 93 in the nucleon-nucleon centre-of-mass frame. Their production is studied as a function of two measures of event activity, namely the charged-particle multiplicity measured in the pseudorapidity interval | η | < 2 . 4, and the sum of transverse energy deposited at forward pseudorapidity, 4 . 0 < | η | < 5 . 2. The Y cross sections normalized by their event activity integrated values, Y (nS) / 〈 Y (nS)〉, are found to rise with both measures of the event activity in pp and pPb. In both collision systems, the ratios of the excited to the ground state cross sections, Y (nS) / Y (1S), are found to decrease with the charged-particle multiplicity, while as a functi ... mehron of the transverse energy the variation is less pronounced. The event activity integrated double ratios, [ Y (nS) / Y (1S)] pPb / [ Y (nS) / Y (1S)] pp , are also measured and found to be 0 . 83 ± 0 . 05 (stat . ) ± 0 . 05 (syst . ) and 0 . 71 ± 0 . 08 (stat . ) ± 0 . 09 (syst . ) for Y (2S) and Y (3S), respectively.