The morphological and rheological properties of a commercial propylene-ethylene copolymer (PEC) and a series of blends with different concentrations of poly (ethylene-co-propylene) are investigated. The blends are prepared mixing PEC with fractions obtained from it by solvent extraction. The phase structure of samples exposed to different thermal and mechanical histories was analyzed using scanning electron microscopy. The linear viscoelastic properties of the molten polymers were measured using different test sequences that include dynamic frequency and time sweeps. The phase structure of most blends changes dramatically with time when the polymers are kept in the molten state due to the coalescence of the domains. For example, the initial morphology of PEC which presents domains of similar to 1 mu m diameter changes to regions of more than 10 mu m of average diameter after 90 min at 178 degrees C at rest. Coincidentally, the dynamic moduli of the blends change during annealing reaching values that depend on the mechanical history. For example, the elastic modulus of PEC increases similar to 32% during a dynamic time sweep of 45 min using a frequency of 0.1 s(-1), while it decreases similar to 18% when a frequency of 1 s(-1) is applied. Moreover, the modulus measured at 0.1 s(-1) of samples annealed at rest during 45 min is similar to 8% larger than that of the fresh material.