The a-c conductivity of a weakly ionized plasma can be calculated by making a spherical harmonic expansion of the electron velocity distribution function. This conductivity determines the propagation characteristics of rf waves in the plasma. If the plasma is immersed in a d-c magnetic field, the isotropic part of the distribution function depends upon the polarization of the rf wave; that is, it depends upon how the electromagnetic energy is divided among the right and left circularly polarized modes and the longitudinal mode. When the magnetic field is reduced to zero, the function reduces to the form first derived by Margenau. A closed form expression for the function can be obtained for the case of a constant electron mean free path. A nonlinear conductivity tensor can be derived in which each component is a function of the polarization of the local rf field. Curves of the conductivity tensor components in the principal coordinate system as a function of the energy in the right and left circular modes are presented for propagation along the magnetic field. (Author).