  Since the gauge group underlying 2+1-dimensional general relativity is
non-compact, certain difficulties arise in the passage from the connection to
the loop representations. It is shown that these problems can be handled by
appropriately choosing the measure that features in the definition of the loop
transform. Thus, ``old-fashioned'' loop representations - based on ordinary
loops - do exist. In the case when the spatial topology is that of a two-torus,
these can be constructed explicitly; {\it all} quantum states can be
represented as functions of (homotopy classes of) loops and the scalar product
and the action of the basic observables can be given directly in terms of
loops.
