  Type A surfaces are the locally homogeneous affine surfaces which can be
locally described by constant Christoffel symbols. We address the issue of the
geodesic completeness of these surfaces: we show that some models for Type A
surfaces are geodesically complete, that some others admit an incomplete
geodesic but model geodesically complete surfaces, and that there are also
others which do not model any complete surface. Our main result provides a way
of determining whether a given set of constant Christoffel symbols can model a
complete surface.
