The two-dimensional speckle field and the phase produced by the Gaussian correlation random surfaces on the Fraunhofer plane were simulated. It was found that the zero-contour of the real and imaginary parts can be in the tangent and superposition situations besides the traditional intersection situation. The tangential points and the superposition-lines can also form phase singularities, around which the phase distribution shows the characteristics of discontinuity and symmetry and differs from the spiral distribution around the traditional singular points formed by the zero crossings of the real and imaginary parts. With the propagation of the optical wave, the relative positions of the zero-contour of the real and imaginary parts change from tangent to superposition, and then to intersection on the different observation plane with the simultaneously changes of the the phase singularities.