In this paper, we discuss the evolution of the offwaist incident Gaussian beam in the nonlocal nonlinear media by use of the (1+1)dimensional strongly nonlocal model. An exact analytical solution for the evolution is obtained. We find that no matter how high the power of the incident beam is, the beam width will oscillate periodically and no spatial soliton will exist, which is substantially different from the onwaist incident case. The influence of the input power and incident position on beam evolution is also discussed. The higher the input power, the narrower the beam width is. The incident position determines the initial evolution trend. The definition of a “spatial chirp” is given, to our knowledge, for the first time. The physical origin of the above phenomenon is that the different incident position corresponds to the different spatial chirp. The concept of the spatial chirp provides a new physical qualitative insight into the evolution of optical beams. The comparisons of beam evolutions in focusing media, in defocusing media and in linear homogeneous media are also given.