The exclusive deep inelastic electroproduction of psi(2S) and J/psi (1S) at an ep centre-of-mass energy of 317 GeV has been studied with the ZEUS detector at HERA in the kinematic range 2 < Q(2) < 80 GeV2, 30 < W < 210 GeV and vertical bar t vertical bar < 1 GeV2, where Q(2) is the photon virtuality, W is the photon-proton centre-of-mass energy and t is the squared four-momentum transfer at the proton vertex. The data for 2 < Q(2) < 5 GeV2 were taken in the HERA I running period and correspond to an integrated luminosity of 114 pb(-1). The data for 5 < Q(2) < 80 GeV2 are from both HERA I and HERA II periods and correspond to an integrated luminosity of 468 pb(-1). The decay modes analysed were mu(+)mu(-) and J/psi(1S)pi(+)pi(-) for the psi(2S) and mu(+)mu(-) for the J/psi(1S). The cross-section ratio sigma(psi(2S))/sigma(J/psi(1S)) has been measured as a function of Q(2), W and t. The results are compared to predictions of QCD-inspired models of exclusive vector-meson production. (C) 2016 The Author(s). Published by Elsevier B.V.