Angular correlations between unidentified charged trigger particles and various species of charged associated particles (unidentified particles, pions, kaons, protons and antiprotons) are measured by the ALICE detector in p-Pb collisions at a nucleon-nucleon centre-of-mass energy of 5.02 TeV in the transverse-momentum range 0.3 < p(T) < 4 GeV/c. The correlations expressed as associated yield per trigger particle are obtained in the pseudorapidity range vertical bar n(lab)vertical bar < 0.8. Fourier coefficients are extracted from the long-range correlations projected onto the azimuthal angle difference and studied as a function of p(T) and in intervals of event multiplicity. In high-multiplicity events, the second-order coefficient for protons, 4, is observed to be smaller than that for pions, v(2)(pi), up to about p(T) = 2 GeV/c. To reduce correlations due to jets, the per-trigger yield measured in low-multiplicity events is subtracted from that in high-multiplicity events. A two-ridge structure is obtained for all particle species. The Fourier decomposition of this structure shows that the second-order coefficients for pions and kaons are similar. The v(2)(p) is found to be smaller at low P-T and larger at higher p(T) than v(2)(pi), with a crossing occurring at about 2 GeV/c. This is qualitatively similar to the elliptic-flow pattern observed in heavy-ion collisions. A mass ordering effect at low transverse momenta is consistent with expectations from hydrodynamic model calculations assuming a collectively expanding system. (C) 2013 CERN. Published by Elsevier B.V. All rights reserved.72641699164177