[en] The influence of resonance production in relativistic hadron-hadron and nucleus-nucleus collisions, and their role in explaining the so-called 'anomalous' behaviour of the hadronic transverse momentum spectra at low p_T, is studied qualitatively and quantitatively in the framework of a simple thermodynamical model. In the discussion effects from the different kinematics in 2- and 3-body decays and from the finite width of the resonances are included. We compare our results with data from the NA35 collaboration for pion, kaon, proton and Λ p_T-spectra from 200 A GeV S+S collisions and with pp data at similar energies. The model can successfully describe both S+S and pp data, with T=200 MeV, μ_b=200 MeV and T=180 MeV, μ_b=250 MeV, respectively. We discuss the consistency of these parameters by comparing with measured particle ratios and checking the freeze-out conditions. We conclude that the low-p_T part of the pion spectra is dominated by resonance decays, and that there is no low-p_T 'anomaly'. We also find, that the flattening of the high-p_T tail in central nuclear collisions compared to pp data is probably not of thermal origin but caused by other effects, e.g. collective transverse flow. (orig.)