This thesis is concerned with the study by solid-state NMR of the polymers formed by acid anhydride/hydroxyl cross-linking systems. The polymers studied in this thesis are based on a copolymer containing either itaconic or maleic anhydride which cross-Jinks with a polyester tipped with triethanolamine. The mobility of the polyester chains in the cross-linked films is probed by solid-state NMR, and the kinetics of the cure between acid anhydride/hydroxyi systems is discussed. The degradation of the cross-Jinked films is studied by (^13)C solid-state NMR. The films are shown to undergo hydrolysis when subjected to their exposure environment. The theory behind transient nuclear Overhauser effects in the solid state is discussed, and comparisons are made between the theoretical simulations and the experimented data for the cross—linked films. Lastly, a solid-state heteronuclear NOESY experiment is presented for a (^13)C(_2)-enriched acid anhydride/hydroxyl cross-linked film.