  We analyzed the problem of finding a surfaces family through an asymptotic
curve with Cartan frame. We obtain the parametric representation for surfaces
family whose members have the same as an asymptotic curve. By using the Cartan
frame of the given null curve, we present the surface as a linear combination
of this frame and analysed the necessary and sufficient condition for that
curve to satisfy the asymptotic requirement. We illustrate the method by giving
some examples.
