At present, cis-1,3,4,6-tetranitro-octahydroimidazo-[4,5-d]imidazole (bicyclo-HMX, BCHMX) and epsilon-2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (epsilon-HNIW, CL-20) are a topic of interest from the attractive and the potentially attainable nitramines. They were chosen to be studied in comparison with 1,3,5-trinitro-1,3,5-triazinane (RDX) and -1,3,5,7-tetranitro-1,3,5-tetrazocane (-HMX). Marginal attention is devoted also to 4,8,10,12-tetranitro-2,6-dioxa-tetraazawurtzitane (Aurora 5). BCHMX, epsilon-HNIW, RDX, and HMX were studied as plastic bonded explosives (PBXs) with elastic properties based on Composition C4 and Semtex 10 matrices. Also they were studied as a highly pressed PBXs based on the Viton A binder. The detonation parameters and sensitivity aspects of these nitramines and their corresponding PBXs were determined. Relative explosive strengths (RS) of these compositions are mentioned with mutual relationships between the measured RS values and some detonation parameters. These relationships indicate a possibility of changes in detonation chemistry of these mixtures filled mainly by HNIW. A sensitivity of RS-CL20 (HNIW with reduced sensitivity) is reported and the new findings in the friction sensitivity are discussed.