Abstract We consider a model of thermalisation of pions due to elastic scattering and define the region of applicability of this model. In this region the chemical potential is positive. We analyse the absorptive and dispersive properties of pions during thermalisation, by calculating the pion collective potential. The pion gas can be thermally equilibrated but it will be out of chemical 3quilibrium. We define the degree of thermalisation near freeze-out at the level ∼ 70% for S + S and ∼ 90% for O + Au collisions at CERN. We find that the effect of the chemical potential in pion spectra is stronger than the temperature effect at p ⊥ ⩽ 200 MeV.