The deflagration-to-detonation transition (DDT) in hot, thermally damaged HMX (5-phase) and HMX-based polymer-bonded explosives (PBX 9501, LX-14, LX-10 and PBX 9012) differs in some respects from what has been observed in similar tests (DDT tube experiments) with room temperature granular explosives. We provide streak images with other observations and demonstrate the behavior can be binned according to the degree of porosity evolved from physical and chemical damage to the compositions. In each bin, the DDT behavior eventually organizes to resemble Type I DDT, but differs in the early-stage burn phenomena and how a propulsive thermal explosion event arises. We argue that the hot explosive properties, such as permeability and compressibility, and the morphological characteristics of the thermal damage, control the physical mechanism for establishment of the thermal explosion. In some cases, these observations may need to be carefully implemented in numerical models to increase predictive value for these materials at elevated temperature. With high-porosity (phi approximate to 20-50%), the PBXs behaved like gran- ular beds. At intermediate levels of porosity (phi approximate to 4-20%), the transition occurred over longer distances and the process is characterized by a weak, slow convective burn precursor that sets up thermal run- away to explosion behind the flame infiltration front. In the low-porosity bin (phi approximate to 0-4%), where run lengths were short, the thermal explosion is the result of compressive, and possibly also, deconsolidative burning. It is clear that the high-temperature conditions imposed in these experiments caused sensitization towards DDT and this effect was most apparent in tests where the explosive was heated until runaway and auto-ignition where transition distances were among the shortest measured. Practical findings include there being some safety benefit for having binders in HMX formulations, especially when the binder is thermally stable. (C) 2020 The Combustion Institute. Published by Elsevier Inc. All rights reserved.