CERN-LHC. The nuclear modification factors of J/psi and psi(2S) mesons are measured in PbPb collisions at a centre-of-mass energy per nucleon pair of 5.02 TeV. The analysis is based on PbPb and pp data samples collected by CMS at the LHC in 2015, corresponding to integrated luminosities of 464 inverse microbarns and 28 inverse picobarns, respectively. The measurements are performed in the dimuon rapidity range of abs(y)< 2.4 as a function of centrality, rapidity, and transverse momentum (pT) from pT= 3 GeV/c in the most forward region and up to 50 GeV/c. Both prompt and nonprompt (coming from b hadron decays) J/psi mesons are observed to be increasingly suppressed with centrality, with a magnitude similar to the one observed at 2.76 TeV for the two J/psi meson components. No dependence on rapidity is observed for either prompt or nonprompt J/psi mesons. An indication of a lower prompt J/psi meson suppression at pT > 25 GeV/c is seen with respect to that observed at intermediate pT. The prompt psi(2S) meson yield is found to be more suppressed than that of the prompt J/psi mesons in the entire pT range.