DeBra-Delp satellite refers to a particular attitude with respect to the orbital coordinates of certain rigid three-axis satellites. The attitude stability of such a satellite placed on a circular orbit, examples of which can be found among natural and artificial satellites, is examined. As is well known, linearized techniques for the stability of the particular equilibrium of the named satellites have been inconclusive because no Lyapunov function for them was found. Our aim is to demarcate a region in the parameter space (T-1, T-2) defined by the moments of inertia, where the equilibrium of DeBra-Delp satellites is stable. This aim is achieved using and contrasting both analytical and numerical solutions and analyzing nonlinear characteristics of the problem. The analytical approach used is based on Tkhai's theorem, which represents an extension of the KAM theory and provides a sufficient criterion for stability.