A new method of solving the Boltzmann equation for a degenerate Fermi system is described and compared with the approximation of Abrikosov and Khalatnikov and with variational calculations. The first two terms in the expansions of the inverse relaxation times in powers of the absolute temperature are calculated, and the resulting expressions are applied to dilute mixtures of ${\mathrm{He}}^{3}$ in liquid ${\mathrm{He}}^{4}$ and to nearly ferromagnetic Fermi liquids.