  We reveal the relevance between the nonlocality and the focusing/defocusing
states in nonlocally nonlinear media, and predict a novel phenomenon that the
self-focusing/self-defocusing property of the optical beam in the nonlocally
nonlinear medium with a sine-oscillation response function depends on its
degree of nonlocality. The transition from the focusing nonlinearity to the
defocusing nonlinearity of the nonlinear refractive index will happen when the
degree of nonlocality of the system goes cross a critical value, and vise
verse. Bright and dark soliton solutions are obtained, respectively, in the
focusing state and in the defocusing state, and their stabilities are also
discussed. It is mentioned that such a phenomenon might be experimentally
realized in the nematic liquid crystal with negative dielectric anisotropy or
in the quadratic nonlinear medium.
