In this article, we report the results of molecular dynamics simulations for models of poly(ethylene), isotactic poly(propylene), and mixtures of the two to understand the possible origin of melt state incompatibility. At temperatures well above the crystal melting points of the homopolymers, isolated poly(ethylene) and poly(propylene) chains formed high-density collapsed states. The poly(ethylene) and poly(propylene) chains were found to segregate into distinct domains even when the initial state was highly interpenetrating. The poly(ethylene) phase shows a significant amount of focal order at the simulation temperature. In the case of poly(propylene), some helical segments were found in the collapsed structure. We speculate that the immiscibility of these two nonpolar polymers, in the melt state, may be due to the differences in local morphology that are present in the melt state.