Preparation of glycidyl azide polymer (GAP) and its influence on the stability and explosive properties of polymer bonded explosives (PBXs) based on several cyclic nitramines, namely β-1,3,5,7-tetranitro-1,3,5,7-tetrazocane (β-HMX), 1,3,5-trinitro-1,3,5-triazinane (RDX), ε-2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (ε-CL-20) and cis-1,3,4,6-tetranitrooctahydroimidazo-[4,5-d]imidazole (BCHMX) are discussed. Impact and friction sensitivity were determined. Combustion heat and detonation velocity of the studied samples were measured. The detonation parameters were obtained by the EXPLO 5 thermodynamic code. The compatibility between the energetic polymeric matrix and the studied nitramines was discussed following a vacuum stability test. The relationship between performance and sensitivity was studied in comparison with literature HTPB compositions. The results showed that the GAP matrix increased both the detonation velocities of its PBXs by more than 500 m s⁻¹ and the heat of explosion by nearly 1.13–1.16 times in comparison to PBXs based on HTPB for each individual explosive. The compatibility of BCHMX to the GAP matrix seems to be better than that of CL-20/GAP.