Two mechanisms are considered which contribute to the observed thermal expansion of the N₂-O₂ solid solution. One of them, connected with the renormalisation of the effective spin-figure coupling constant by the spin-libron interaction, is linear in impurity O₂ concentration. The second one is due to formation of clusters of exchange-bound molecules and in the case of pair clusters is quadratic in concentration. The contributions from both the mechanisms are equalised for the O₂-molecule concentration of about 1%. The data on the O₂-O₂ exchange interaction is obtained from comparison between the theoretical and experimental results on the excess thermal expansion of the N₂-O₂ solid solution. The theoretical model permits the explanation of the main features of the observed anomalies, but only a more sophisticated theory will be able to give a close fit to the experiment.