Annealing experiments have been carried out just below the melting temperature of both polyethylene (LLDPE) and polypropylene (PP) and their blends. The total melting enthalpy measured after the annealing cycle was greater by 10-15% with respect to the value having been measured before it. During the annealing period the heat capacity decreases to a lower value within the first 2-3 min. Heat capacities of PP (either in pure form or in the blends) measured during the heating cycle following the annealing cycle have the same value as during the cooling section. The heat capacities of the LLDPE in the heating cycle following the annealing were those of the preceding heating cycle. The total heat flows in the cooling section following the annealing cycle were greater than those in another cooling cycle at the same temperatures indicating that the crystallisation takes place during the cooling rather than during the annealing periods. The presence of LLDPE decreases the crystallisation temperature of PP. The presence of SEBS in the blend results in a greater crystallisation temperature than that of pure PP. The crystallisation temperature of LLDPE increases with increasing levels of PP.