Muon spin relaxation has been measured in longitudinal and zero field configurations for a number of conducting polymers in the polypyrrole and polyaniline families. The measurements have been made as a function of temperature down to 11K and in applied fields up to 2000G. Hyperfine parameters have been deduced for the coupling between muon and polaron spins and the spin dynamics has been modeled on the basis of polaron diffusion, which has one-dimensional character at low temperatures, becoming more two-dimensional at room temperature.