Spherical supported vesicles (SSVs), a new model system consisting of single dimyristoyl phosphatidylcholine (DMPC) bilayers adsorbed to spherical glass beads with a narrow size distribution, were prepared at two different sizes (0.5 and 1.5 microns) and their physical properties were studied by deuterium nuclear magnetic resonance (2H-NMR). Such SSV samples can be prepared at any desired size between 0.3 and 10 microns. The 2H-NMR measurements provide evidence for a strong dependence of the spectra and the transverse relaxation times on the curvature of the SSVs in a diameter range between 0.5 and 1.5 microns. For larger SSVs (1.5 microns diameter) their powder spectra and their calculated oriented spectra are similar to those obtained for multilamellar dispersions of DMPC-d54. The lineshape of the smaller SSVs exhibits a temperature dependence which is not found in multilamellar samples. The SSVs are stable in the liquid crystalline phase over days but irreversibly change to multilamellar vesicles in the gel state. The average thickness of the water layer between the single bilayer and the glass bead surface was estimated by 1H-NMR to e 17 +/- 5 A.