The research paper under consideration investigates the motion in the vicinity of triangular equilibrium points of the circular restricted three-body problem of a passively gravitating dust particle in the gravitational field for the binaries system (Kruger 60 and Achird). The two bodies of the binary are both oblate radiating stars possessing P-R drag. The position of triangular equilibrium points of the particle is seen to be affected by oblateness, radiation and P-R drag. In our numerical exploration of the binary system Kruger 60 and Achird, we computed the radiation factors q (i= 1,2) and the velocity of light c which is a component of the P-R drag. The points are unstable due to the presence of a positive real part of the complex roots.