  In this paper we consider the Blaschke's asymptotic lines (also called affine
asymptotic lines) of regular surfaces in 3-space. We study the binary
differential equations defining Blaschke's asymptotic lines in the elliptic and
hyperbolic regions of the surface near affine cusp points and to at affine
umbilic points. We also describe the affine asymptotic lines near the Euclidean
parabolic set including the Euclidean flat umbilic points.
