The cure reactions, chemical structure, and network topography of diaminodiphenyl sulfone (DDS)-cured tetraglycidyl 4,4′diaminodiphenyl methane (TGDDM) epoxies are reported. Systematic Fourier transform infrared (FTIR) spectroscopy studies of the cure and degradation reactions of TGDDM-DDS epoxies in the 100–300°C temperature range as a function of DDS and boron trifluoride monoethylamine, BF3: NH2C2H5 catalyst concentrations are presented. FTIR studies indicate TGDDM epoxide homopolymerizes in the 175–250°C range via epoxide-hydroxyl (E-OH) chain extension reactions. The hydroxyl groups are initially present as α-glycol impurities or are formed by epoxide isomerization and/or oxidation. Three principal cure reactions occur at 177°C for TGDDM-DDS epoxies, namely primary amine-epoxide (PA-E), secondary amine-epoxide (SA-E) and E-OH reaction with the PA-E reaction being an order of magnitude faster than the other two cure reactions. The PA-E reaction dominates the early stages of cure and, hence, composite processing conditions. The three cure reactions are catalyzed to similar extents by BF3: NH2C2H5. FTIR and molecular modeling studies indicate that the E-OH and SA-E reactions can occur intermolecularly to form crosslinks or intramolecularly to form non-cross-linked internal rings. The complex degradation reactions of TGDDM-DDS epoxies in the 177–300°C range are reported. The principal degradation reactions involve (1) dehydration and/or oxidation to form ether crosslinks and (2) decomposition of the EOH cure reaction products to form propenal. Based on a knowledge of the cure reactions, together with molecular modeling, the chemical structure and network topography of TGDDM-DDS epoxies are reported.