Solid state Cd-113, Se-77, C-13 and P-31 NMR have been used to study a number of Cd chalcogenide nanoparticles synthesized in tri-n-octyl-phosphine (TOP) with different compositions and architectures. The pure CdSe and CdTe nanoparticles show a dramatic, size-sensitive broadening of the Cd-113 NMR line, which can be explained in terms of a chemical shift distribution arising from multiple Cd environments. From C-13 NMR, it has been discovered that TOP, or its derivatives such as TOPO ( trioctylphosphine oxide), is rapidly moving about the surface of the nanoparticles, indicating that it is relatively weakly bound as compared to other materials used as surface ligands, such as hexadecylamine. P-31 NMR of the nanoparticles shows at least five species arising from coordination of the ligands to different surface sites. Cd-113 NMR of CdSeTe alloy and layered nanoparticles has provided crucial information which, in conjunction with results from other techniques (especially optical characterization), has made it possible to develop a detailed picture of the composition and structure of these materials: (i) a true CdSeTe homogeneous alloy nanoparticle,(ii) a nanoparticle segregated into an alloy core region rich in Te, with a CdSeTe (close to 1 : 1 Se : Te) alloy shell and (iii) a CdSe/CdTe/CdSe layered nanoparticle in which the CdTe layer contains a small amount of Se and which forms a Quantum Dot Quantum Well (QDQW) system. The results demonstrate that solid state NMR is a vital tool in the arsenal of characterisation techniques available for nanomaterials.