Bulk longitudinal spin relaxation time T-1 has been studied in hyperpolarised liquid He-3-He-4 mixtures at saturated vapour pressure and at low magnetic field (2 mT). Wall relaxation is efficiently prevented by using a cesium-coated glass cell, and T(1)s as long as 10h have been observed. T-1 is found to vary with He-3 density n(3) as n(3)(alpha) with alpha = -0.90 +/- 0.02 at T = 1.1 K. This was obtained for several densities it, ranging from 0.07 to 11 mol/l, which correspond to He-3 concentrations alpha(3) ranging from 0.20 to 34%. An increase of T-1 with increasing temperature has also been observed at x(3) = 8% from 2 to 3.7 K, as expected in the non-degenerate regime. (C) 2000 Elsevier Science B.V. All rights reserved.