  Renormalisation group (RG) equations in two-dimensional N=1 supersymmetric
field theories with boundary are studied. It is explained how a manifestly N=1
supersymmetric scheme can be chosen, and within this scheme the RG equations
are determined to next-to-leading order. We also use these results to revisit
the question of how brane obstructions and lines of marginal stability appear
from a world-sheet perspective.
