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Nonlinear approximation of periodic motions around the collinear equilibrium points in the case of the restricted three-body problem when the angular velocity of the primaries is not equal to the value of the classical problem (which is unit in the usual units of mass, length and time), is studied. The stability of the equilibrium points and the analytical solutions in their neighborhood constructing series approximations of the periodic orbits in the planar and in the spatial problem, aredoi:10.1051/0004-6361:20041216 fatcat:5bio4l3rebgb7pek5y24ynctze