The proton and deuterium longitudinal relaxation rates were studied at room temperature up to the highest protein concentrations in oxyhaemoglobin solutions of different H2O/D2O composition. The deuterium relaxation rates followed the experimentally well known single linear dependence on protein concentration, the slopes being little influenced by solvent (D2O/H2O) composition. The proton relaxation rates show two different linear dependences on haemoglobin concentration. The entire concentration range is described by two straight lines with the threshold concentration about 11 mM (in haem). The ratio of the slopes is 1.6 (high-to-low HB-conc). Only in the higher concentration range two T1's were observed if the solvent contained more than half of D2O. The slow relaxation phase of protons has T1's similar to those measured in solutions with less than half of D2O. The relaxation of the other phase was ten times faster. The ratio of the proton populations in these two phases was equal to 2 (slow-to-fast) and independent of protein concentration. The fast relaxing protons are attributed to water molecules encaged within two or more haemoglobin molecules which associate for times long enough on the PMR time-scale.