  We study symmetric affine surfaces which have non-vanishing torsion tensor.
We give a complete classification of the local geometries possible if the
torsion is assumed parallel. This generalizes a previous result of Opozda in
the torsion free setting; these geometries are all locally homogeneous. If the
torsion is not parallel, we assume the underlying surface is locally
homogeneous and provide a complete classification in this setting as well.
