  We consider simple CFT models which contain massless bosons, or massless
fermions or a supersymmetric combination of the two, on the strip. We study the
deformations of these models by relevant boundary operators. In particular, we
work out the details for a boundary operator with a quadratic dependence on the
fields and argue that some of our results can be extended to a more general
situation. In the fermionic models, several subtleties arise due to the
doubling of zero modes at the UV fixed point and a ``GSO projected'' RG flow.
We attempt to resolve these issues and to discuss how bulk symmetries are
realised along the flow. We end with some speculations on possible string
theory applications of these results.
