  We study approximate solutions of the gravitational lens equation and
corresponding lens magnification factor near the critical point. This
consideration is based on the Taylor expansion of the lens potential in powers
of coordinates and an introduction of a proximity parameter characterising the
closeness of a point source to the caustic. Second-order corrections to known
approximate solutions and magnification are found in case of a general fold
point. The first-order corrections near a general cusp are found as well. Key
words: gravitational lensing, methods: analytical
