Transverse momentum (p sub(T)) distributions of identified hadrons produced in p-Pb collisions at radicals sub(NN) = 5.02 TeV have been measured at mid-rapidity (0 < y sub(CMS) < 0.5) by ALICE. Particle tracks are reconstructed using the central barrel detectors. Particle identification is performed via specific energy loss, time-of-flight or their characteristic decay topology over a wide transverse momentum range (0 GeV/c up to 8 GeV/c). Spectral shapes and particle ratios are measured in six multiplicity classes. They are compared with several model calculations and results from Pb Pb collisions at radicals sub(NN) = 2.76 TeV and pp collisions at radicals sub(NN) = 7 TeV at the LHC. The results are discussed with respect to possible collective effects in p-Pb collisions.