This study concerns mixtures of triacetone triperoxide (3,3,6,6,9,9-hexamethyl-1,2,4,5,7,8-hexoxonane, TATP) and ammonium nitrate (AN) with added water (W), as the case may be, and dry mixtures of TATP with urea nitrate (UN). Relative performances (RP) of the mixtures and their individual components, relative to TNT, were determined by means of ballistic mortar. The detonation energies, E-0, and detonation velocities, D, were calculated for the mixtures studied by means of the thermodynamic code CHEETAH. Relationships have been found and are discussed between the RP and the E0 values related to unit volume of gaseous products of detonation of these mixtures. These relationships together with those between RP and oxygen balance values of the mixtures studied indicate different types of participation of AN and UN in the explosive decomposition of the respective mixtures. Dry TATP/UN mixtures exhibit lower RP than analogous mixtures TATP/AN containing up to 25% of water. Depending on the water content, the TATP/AN mixtures possess higher detonability values than the ANFO explosives. A semi-logarithmic relationship between the D values and oxygen coefficients has been derived for all the mixtures studied at the charge density of 1000 kg m(-3). Among the mixtures studied, this relationship distinguishes several samples of the type of "tertiary explosives" as well as samples that approach "high explosives" in their performances and detonation velocities. (C) 2007 Published by Elsevier B.V.