The evolution of the incoherent superposition of two nonparaxial Gaussian beams carried a C-dipole was theoretically and numerically studied. The results show that the position and degree of polarization of two C-points may change with variation of the relevant parameters. The slope of the axis of the C-dipole increases monotonically with propagation. For the case of non-paraxial beams, creation and annihilation of C-dipoles occur as the beams propagate to 0.01zR and 10.39zR, respectively. At the plane z=zR, the creation and annihilation of C-points respectively occurs when the waist width increases to 0.222μm and 0.56μm. Besides, the creation and annihilation of C-points may take place with variation of the off-axis parameter and the wavelength of the host nonparaxial beams. The results would be useful for deeply understanding singular optics and seeking for their potential applications.