The R⁴-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 special holonomy. Nevertheless, in many such cases, including Calabi-Yau compactifications of string theory and G₂-compactifications of M-theory, it has been shown that because of associated corrections to the supersymmetry transformation rules, the deformation remains supersymmetric. In this talk, we consider Spin(7) compactifications of string theory, showing that again supersymmetry survives, despite the loss of Spin(7) holonomy in the deformed background. We also consider the deformations of Spin(7) backgrounds in M-theory, showing that supersymmetry is also maintained. Finally, we consider the intrinsically M-theoretic case of compactifications on 10-manifolds of SU(5) holonomy. We obtain the corrected solutions, and discuss their supersymmetry.