  Higher-derivative terms in the string and M-theory effective actions are
strongly constrained by supersymmetry. Using a mixture of techniques, involving
both string amplitude calculations and an analysis of supersymmetry
requirements, we determine the supersymmetric completion of the R^4 action in
eleven dimensions to second order in the fermions, in a form compact enough for
explicit further calculations. Using these results, we obtain the modifications
to the field transformation rules and determine the resulting field-dependent
modifications to the coefficients in the supersymmetry algebra. We then make
the link to the superspace formulation of the theory and discuss the mechanism
by which higher-derivative interactions lead to modifications to the
supertorsion constraints. For the particular interactions under discussion we
find that no such modifications are induced.
