Multiplicity moments of charged particles in deep inelastic e+p scattering have been measured with the ZEUS detector at HERA using an integrated luminosity of 38.4 pb-1. The moments for Q2 > 1000 GeV2 were studied in the current region of the Breit frame. The evolution of the moments was investigated as a function of restricted regions in polar angle and, for the first time, both in the transverse momentum and in absolute momentum of final-state particles. Analytic perturbative QCD predictions in conjunction with the hypothesis of Local Parton-Hadron Duality (LPHD) reproduce the trends of the moments in polar-angle regions, although some discrepancies are observed. For the moments restricted either in transverse or absolute momentum, the analytic results combined with the LPHD hypothesis show considerable deviations from the measurements. The study indicates a large influence of the hadronisation stage on the multiplicity distributions in the restricted phase-space regions studied here, which is inconsistent with the expectations of the LPHD hypothesis. © 2001 Published by Elsevier Science B.V.