Cocrystallization in blends of linear and branched polyethylenes has been studied under both isothermal and slow-cooling crystallization conditions. Before the more common, polydisperse-type polyethylenes were studied and the results analysed, model systems were investigated in detail. The components used in the model binary blends were molecular weight fractions of linear polyethylene, hydrogenated poly(butadiene) as a model for the ethylene-1-alkene copolymers, and a three-arm star hydrogenated poly(butadiene) as a model for the long chain branched polyethylenes. It was found that a key factor in governing the extent of cocrystallization in these blends is the closeness of crystallization rates of each of the components. The extent of the cocrystallization thus diminishes with increasing concentration of the linear component in the blend. It is found that copolymer composition and molecular structure also have a strong influence on cocrystallization. The amount of cocrystallization is favoured at the lowest isothermal crystallization temperatures and is maximized under quenching conditions. The general features that influence cocrystallization, which have evolved from this study, are discussed.