  We consider the general problem of constructing the structure of a smooth
manifold on a given space of loops in a smooth finite dimensional manifold. By
generalising the standard construction for smooth loops, we derive a list of
conditions for the model space which, if satisfied, mean that a smooth
structure exists.
  We also show how various desired properties can be derived from the model
space; for example, topological properties such as paracompactness. We pay
particular attention to the fact that the loop spaces that can be defined in
this way are all homotopy equivalent; and also to the action of the circle by
rigid rotations.
