Experimental evidence is reached by differential scanning calorimetry (DSC), and modulated differential scanning calorimetry (MDSC), about the existence of a glass transition in a commercial ethylene-1-octene copolymer synthesized with a metallocene catalyst and in its corresponding composites with glass fibre at different content of reinforcement. The glass transition is found in the region from -50 to -45 degreesC depending upon the empirical protocol. Its location is quite independent on the fibre content. The presence of reinforcement in the polymeric matrix has some influence on the crystalline regions, since slightly more perfect crystals seem to be obtained in the composites with not very high glass fibre content, judging from the better resolution of the (110) diffraction and from the slightly higher melting temperatures. However, the normalized crystallinity remains practically unchanged in all the samples.