Measurements of the nuclear magnetic spin-lattice relaxation time T 1 of liquid 3 He containing 0.5% 4 He and of 3 He-4 He mixtures as a function of magnetic field up to 22 T and at temperatures down to 40 mK show a new surface relaxation mechanism for liquid 3 He, which is proportional to the square of the magnetic field and can be described by classical relaxation theory. The intrinsic relaxation time of liquid 3 He, obtained from T 1 measurements by eliminating the surface relaxation contribution, is in good agreement with existing Fermi liquid theory. [S0031-9007(97)03546-1]