We have considered the effect due to the presence of two-temperature electrons on the formation and propagation of cnoidal waves in a weak relativistic plasma. Since the cnoidal wave is equivalent to an infinite series of solitary waves, it is worthy of study for the situation where more than one solitary wave is important. The phase velocity of the modulated periodic wave is plotted as a function of the amplitude. The form of the wave for small values of ellipticity of the cnoidal wave shows up as a series of harmonics. Such cnoidal excitations are important in determining the anomalous transport coefficients of a plasma.