The work reports quasielastic neutron scattering (QENS) results on aqueous solutions of trehalose, a biologically and biomedically important disaccharide. We collected data at the Berlin Neutron Scattering Center (BENSC) on alpha,alpha -trehalose deuterated (C12H14O11D8) samples in D2O and on alpha,alpha -trehalose hydrogenated (C12H22O11) samples in H2O at different water content. The employment of selectively deuterated samples allows the separation of the diffusive dynamics of water from that of trehalose. The aim of the work is to furnish new results on the molecular dynamics of trehalose and to investigate the effect of this disaccharide on the neighboring water. This study is part of a comprehensive research effort to understand the molecular processes underlying the bio-protectant effectiveness of the disaccharide using plenty of physical techniques [light scattering, nuclear magnetic resonance (NMR), neutron scattering, thermodynamic measurements]. The data analysis furnishes a microscopic whole-molecule diffusion coefficient in good agreement with NMR results. Furthermore it results that the dynamics of the neighboring water is strongly affected by the presence of trehalose.