The copropagation of two relativistic intense laser beams with orthogonal polarization in a parabolic plasma channel is studied analytically and numerically. A set of coupled equations for the evolution of the laser spot sizes and transverse centroids are derived by use of the variational approach. It is shown that the centroids of the two beams can spiral and oscillate around each other along the channel axis, where the characteristic frequency is determined both by the laser and plasma parameters. The results are verified by direct numerical solution of the relativistic nonlinear Schrödinger equations for the laser envelopes as well as three-dimensional particle-in-cell simulations. In the case with two ultrashort laser pulses when laser wakefields are excited, it is shown that the two wake bubbles driven by the laser pulses can spiral and oscillate around each other in a way similar to the two pulses. This can be well controlled by adjusting the incidence angle and separation distance between the two laser pulses. Preliminary studies show that externally injected electron beams can follow the trajectories of the oscillating bubbles. Our studies suggest a new way to control the coupling of two intense lasers in plasma for various applications, such as electron acceleration and radiation generation.