Abstract In this paper, we have investigated coupled propagation of two coaxially co-propagating and mutually incoherent bright beams in Kerr type nonlinear media, including formation of rhythmic breather pairs. We have proposed existence lines for these rhythmic breather pairs. Moreover, we have also provided a detailed explanation of coupled soliton−breather, breather−breather and breather−soliton pair formation in the parameter space of beam power and beam width ratio. Finally, a law of formation of coupled rhythmic breather pairs has been proposed.