The theological behavior of a branched polymer melt is studied theoretically, based on the extension of the primitive path and tube model We have developed the method to evaluate the stress relaxation moduli and the viscosity of a comb polymer melt and to find out how the result is affected by various improvements in the theory. A carefully calculated form of the path length effective potential is used, including the logarithmic term (which can be derived from a detailed description of the relaxation of a branch) and also allowing for tube dilation (i.e., we take into account that constraint release speeds up reptation). Two qualitatively different types of long-time behavior are predicted, depending on whether the comb backbones are self-entangled or not. Both have already been observed in previously published data.