  In this work we study the affine principal lines of surfaces in 3-space. We
consider the binary differential equation of the affine curvature lines and
obtain the topological models of these curves near the affine umbilic points
(elliptic and hyperbolic). We also describe the generic behavior of affine
curvature lines in the neighborhood of points with double eigenvalues (but not
umbilics) of the affine shape operator and parabolic points
