  We review our recent works on the supersymmetrization of the leading string
correction (the R^4 term) to N=1,2 supergravity theories in four dimensions. We
show that, in the "old minimal" formulations of these theories, when going
on-shell in the presence of this correction, the auxiliary fields which come
from multiplets with physical fields cannot be eliminated, but those ones that
come from compensating multiplets without any physical fields can be
eliminated. We conjecture similar results for other versions of these theories.
