A physical and mathematical model of detonation of aluminum particle gas suspensions of in a wide range of particle sizes from several micrometers to tens of nanometers is presented. In the description of transport properties of particles in the flow and interphase heat transfer, the transition from the continuum regime to the free-molecular regime is considered. The description of aluminum particle combustion is based on the reduced Arrhenius-type kinetics. We take into account the transition from the diffusion type of combustion of large particles to the kinetic type for particles smaller than 1 micrometer. The reaction constants were obtained from the data of experiments on the dependence of the burning time of nano-sized particles on the temperature and pressure of the surrounding gas and the particle diameter. Examples of Chapman-Jouguet detonation structures are given. The boundaries of the applicability of the continual description of thermal dynamics in the detonation of particle suspensions in gas are determined.