Novel highly functional biobased epoxy compounds, epoxidized sucrose esters of fatty acids (ESEFAs), were cross-linked with a liquid cycloaliphatic anhydride to prepare polyester thermosets. The degree of cure or conversion was studied using differential scanning calorimetry (DSC), and the sol content of the thermosets was determined using solvent extraction. The Mechanical properties were studied using tensile testing to determine Young's modulus, tensile stress, and elongation at break. Dynamic mechanical analysis (DMA) was used to determine glass-transition temperature, storage modulus, and cross-link density. The nanomechanical properties of the surfaces were studied using nanoindentation to determine reduced modulus and indentation hardness. The properties of coatings on steel substrates were studied to determine coating hardness, adhesion, solvent resistance, and mechanical durability. Compared with the control, epoxidized soybean oil, the anhydride-cured ESEFAs have high modulus and are hard and ductile, high-performance thermoset materials while maintaining a high biobased content (71-77% in theory). The exceptional performance of the ESEFAs is attributed to the unique structure of these macromolecules: well-defined compact structures with high epoxide functionality. These biobased thermosets have potential uses in applications such as composites, adhesives, and coatings.