The coupling coefficients of cylindrical dielectric resonators with a regular rectangular waveguide under the condition their axes rotation are calculated. The dependences of the coupling coefficients on the angles of rotation and transverse coordinates of the resonator in the case of excitation of the main magnetic types of natural oscillations in them are considered. The dependence of the coupling value on the angles of rotation at the points of circular polarization of the fundamental wave of a rectangular waveguide is shown. The condition for the angle of rotation of the axis of the resonator, determined by the dimensions of the cross section of the waveguide and the frequency of the main type of natural oscillations, is also established, when fulfilled, the coupling coefficient becomes constant in the transverse plane of symmetry of the waveguide. New analytical expressions are derived for the mutual coupling coefficients of identical cylindrical dielectric resonators when their axes rotate relative to a rectangular waveguide. The dependences of the mutual coupling coefficients on the angles of rotation and coordinates of the resonators are investigated. Conditions are found under which the mutual coupling coefficients of two cylindrical resonators are independent of their transverse coordinate in the plane of symmetry of the waveguide. The reasons for the change in the sign of the coupling coefficients of the resonators during their rotation are discussed. The effect of the emergence of coupling extrema for different relative orientations of dielectric resonators is noted. In particular cases of parallelism of the resonator axes of one of the coordinate axes of the waveguide, the analytical expressions found in the work coincide with those obtained earlier. The obtained analytical results make it possible to construct analytical models of bandpass and notch filters, significantly reduce the computation time and optimize complex multi-cavity structures of microwave and optical communication systems.