The structure of the wavefront and transversal optical vortices in an interference field of two off-axis Gaussian beams is studied. It is shown that the positions of phase saddles and vortices depend on the off-axis parameter, beam width, phase and relative amplitude of beams. The saddle can be located inside or outside the vortices. For a certain value of the governing parameter, the saddle point coincides with the vortex. For off-axis beams, the encounters of the saddle point and vortex on both sides in the XZ cross-section do not occur at the same governing parameter η. Moreover, the x value corresponding to the encounter of saddle points is not equal to the x value corresponding to the encounter of vortices.