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 < pT < 4 GeV/c. The correlations expressed as associated yield per trigger particle are obtained in the pseudorapidity range |ηlab| < 0.8. Fourier coefficients are extracted from the long-range correlations projected onto the azimuthal angle difference and studied as a function of pT and in intervals of event multiplicity. In high-multiplicity events, the second-order coefficient for protons, vp2, is observed to be smaller than that for pions, vπ2 , up to about pT = 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 vp2 is found to be smaller at low pT and larger at higher pT than vπ2 , 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.