Detonation waves in gases and in many homogeneous liquid explosives form complex multidimensional structures characterized by detonation cell sizes and regularities that depend on the kinetics of energy release and the thermodynamic parameters of the system. Experimental studies of gaseous detonations (see, for example, [1,2]) and multidimensional numerical simulations of the detonations using a one-step Arrhenius kinetics  have shown that an increase in activation energy leads to more irregular cellular structures. The experiments also indicate that small secondary cells can appear inside the main structure when the activation energy is high enough [1,2]. An analysis [4,5] of similar phenomena in liquid explosives has shown that the secondary cells may occur when the overdriven parts of the cellular detonation front become unstable enough to form secondary triple points during the time between two collisions of the primary triple-shock configurations. Two-dimensional numerical simulations  confirmed that the secondary cellular structure can exist in reactive systems with a one-step Arrhenius kinetics and a high activation energy. The results of numerical simulations presented here show the evolution of the cellular detonations for different activation energies, the formation of different types of the secondary cells, and the influence of the diffusive transport properties which stabilize the detonation front at small scales.