  The R^4-type corrections to ten and eleven dimensional supergravity required
by string and M-theory imply corrections to supersymmetric supergravity
compactifications on manifolds of special holonomy, which deform the metric
away from the original holonomy. Nevertheless, in many such cases, including
Calabi-Yau compactifications of string theory and G_2-compactifications of
M-theory, it has been shown that the deformation preserves supersymmetry
because of associated corrections to the supersymmetry transformation rules,
Here, we consider Spin(7) compactifications in string theory and M-theory, and
a class of non-compact SU(5) backgrounds in M-theory. Supersymmetry survives in
all these cases too, despite the fact that the original special holonomy is
perturbed into general holonomy in each case.
