The problem of detonation-wave structure is studied on the basis of a mathematical model for the detonation of aluminum particles in oxygen within the framework of a single-velocity two-temperature continuum. An analysis of flow types in the form of the Chapman-Jouguet strong-detonation and weak-detonation regimes is given. A chart of the mixture flow regimes in the plane of the Mach number of the detonation wave and the ratio of the characteristic times of thermal relaxation and combustion is constructed using the results of numerical experiments. The domain of realization of only strong detonation regimes, the manifold of existence of weak and strong detonation regimes, and the domain of nonexistence of stationary solutions are determined. The structural properties of the solutions with an internal singular point and weak structurally unstable regimes with a saddle singularity in the final state are described. The stability of all types of stationary regimes against small and finite perturbations that retain the detonation-wave (DW) velocity and the final state is shown by numerical modeling of nonstationary detonation flows.