Molecular dynamics (MD) simulations were carried out to study the solid-state structures of single-site (ss) and Ziegler-Natta (ZN) linear low-density polyethylenes (LLDPE) at a temperature slightly below their melting temperatures. The two bulk state models, used to represent the polymers, possessed the same average branch content ( 10 hexyl branches per 1000 backbone carbons) but with different degrees of interchain branch distribution homogeneity. Both models were first equilibrated at 463 K (i.e., 190 degrees C) for several nanoseconds, and the resultant structures, which were found to be representative of the corresponding liquid-state structures, were then used as the initial structures for the subsequent quenching process. The quenching temperature was 373 K (i.e., 100 degrees C), and the structures were then equilibrated at the same temperature for a period of about 10 ns. The structures of the two polymers formed after the low-temperature equilibrations were considerably different. In particular, the ZN-LLDPE model exhibited a higher amount of order, as quantified by a higher trans/gauche ratio, and a longer "stem length" than those of the ss-LLDPE model. The hexyl branches in the ss-LLDPE model distributed more or less evenly in its interphase and amorphous phase while the branches in the ZN-LLDPE model concentrated in the amorphous phase. The concentration of tie molecules in the ss-LLDPE model was significantly higher than that of ZN-LLDPE. We believe that the structures revealed by the MD simulations correspond to those formed in the early stages of the crystallization process since the models and simulation times used precluded us from modeling the complete crystallization process. However, it is also believed that these structures should resemble the chain conformations of the polymers in their solid state because the available thermal energy at 373 K was not sufficient for further significant conformational rearrangements. The results found are consistent with the experimental findings that ZN-LLDPE solids tend to have a higher degree of crystallinity than ss-LLDPE with similar or even lower average branch content and that ss-LLDPE solids possess a higher concentration of tie molecules. Our simulation results also indicated that with the presence of highly branched chains linear chains tended to crystallize faster than the chains with branches, and this is consistent with the experimental observation of Mirabella that thicker lamellae form before the thinner ones.