Broad-band isothermal dielectric relaxation measurements of anhydrous sucrose were made at ambient pressure in its liquid and glassy states. We found a new secondary relaxation that is slower than the one commonly observed in sugars. Additionally, we carried out the dielectric measurements of the equimolar mixture of D-glucose and D-fructose in wide ranges of temperature and frequency. Comparison of the behavior of these two systems allowed us to make suggestions on the origin of the slower beta-relaxation in sucrose. Computer simulations and coupling model calculations were performed to support our interpretation of the kind of molecular motions responsible for the slower secondary relaxation in the disaccharide considered.