A generalized Flory-Huggins theory is employed to investigate liquid-liquid phase separation in a blend of polydisperse linear and branched polyethylenes (LPE/BPE). A temperature- and concentration-dependent chi parameter is used. The temperature- and composition-dependent coefficients of chi are obtained by fitting to experimental cloud-point data, and having a detailed knowledge of the molecular weight distributions of the two components. The value of chi is found to be small and positive (3.4 x 10(-4) ((phi BPE) = 0.0) to 2.6 x 10(-4) ((phi PBE) = 1.0), T = 423 K) over the temperature composition range of interest, consistent with an approximately athermal blend with small, non-combinatorial entropic contributions to the free energy of mixing. The magnitude of chi determined here is also in reasonable agreement with values measured previously on related systems. The best-fit cloud-point curve obtained for the LPE/BPE blend is a closed immiscibility loop, which is consistent with the experimental observations. However, no critical point(s) or spinodal(s) are found to exist. It is suggested, based on the limited data available, that a blend comprising two monodisperse LPE/BPE components, with molecular weights corresponding to the weight-average molecular weights of the polydisperse linear and branched polyethylenes, would not undergo liquid-liquid phase separation.