  We study how a system of one-dimensional spin-1/2 fermions at temperatures
well below the Fermi energy approaches thermal equilibrium. The interactions
between fermions are assumed to be weak and are accounted for within the
perturbation theory. In the absence of an external magnetic field, spin
degeneracy strongly affects relaxation of the Fermi gas. For sufficiently
short-range interactions, the rate of relaxation scales linearly with
temperature. Focusing on the case of the system near equilibrium, we linearize
the collision integral and find exact solution of the resulting relaxation
problem. We discuss the application of our results to the evaluation of the
transport coefficients of the one-dimensional Fermi gas.
