Abstract. In this Letter, comprehensive results on π ± ,K ± ,K 0 S ,p( ̄ p) and Λ( ̄ Λ) production at mid-rapidity (0 < y CMS < 0 . 5) in p–Pb collisions at √ s NN = 5 . 02 TeV, measured by the ALICE detector at the LHC, are reported. The transverse momentum distributions exhibit a hardening as a function of event multiplicity, which is stronger for heavier particles. This behavior is similar to what has been observed in pp and Pb–Pb collisions at the LHC. The measured p T distributions are compared to d–Au, Au–Au and Pb–Pb results at lower energy and with predictions based on QCD-inspired and hydrodynamic models.