In this paper, we study the problem of finding a family of spacelike surfaces from a given spatial asymptotic curve in Minkowski 3-space. We obtain the parametricrepresentation for a spacelike surface pencil whose members share the same asymptoticspacelike curve as an isoparametric curve. Using the Frenet frame of the given asymptoticcurve, we present the spacelike surface as a linear combination of this frame and analyzethe necessary and sufficient condition for that curve to be asymptotic. The extension tospacelike ruled and developable surfaces is also outlined. We illustrate this method bypresenting some examples.

Keywords: Frenet-Serret formulae, Marching-scale functions, Spacelike asymptotic curve