In the present paper, we calculate the dielectric functions of an ultra-relativistic plasma, such as an electronpositron or a quarkgluon plasma. We use classical transport theory and take into account collisions within the relaxation time approximation. From these dielectric functions we derive the dispersion relations of longitudinal and transverse plasma waves. PACS Nos.: 12.38.Mh, 52.25.Dg, 52.27.Ep, 52.35.Hr