Аннотация
Studied the photogravitational restricted circular three-body problem in which both main gravitating body is radiating. Conducted a complete investigation of the nonlinear stability of the triangular libration points and built their stability areas in the configuration and parameter spaces. For these points in the stability area in the first approximation, except for a set of points corresponding to the resonances of 3rd and 4th orders, almost everywhere there is stability for the majority of initial conditions(in the Lebesgue measure) and formal stability. Shown that for all resonances of order 3 the investigated points are unstable.