Plastic-bonded explosives (PBXs) based on octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) or 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) formulated with the endothermic binders Estane, Viton, or Kel-F exhibit longer times to thermal explosion than do pure HMX and TATB in the one-dimensional time to explosion (ODTX) and in other thermal experiments. Previous chemical kinetic thermal decomposition models for HMX- and TATB- based PBXs assumed that the binders decomposed independently of and at lower temperatures than the explosives. Recent chemical decomposition rate measurements showed that Estane, Viton, and Kel-F are more thermally stable than HMX and TATB. Thus, the longer thermal explosion times for these PBXs are most likely due to endothermic decompositions of the binders by reactions with the gaseous decomposition products of HMX and TATB. New PBX chemical decomposition models are developed using the global HMX and TATB models, measured binder kinetics, and cross-reactions between gaseous explosive products and binders. These new models accurately predict ODTX time to explosion and other experimental data.