  We analyse the constraints from supersymmetry on $ \nabla^4 R^4$ type
corrections to the effective action in $\mathcal{N}=2$ supergravity in eight
dimensions. We prove that there are two classes of invariants that descend
respectively from type IIA and type IIB supergravity. We determine the first
class as $d$-closed superforms in superspace in eight dimensions, whereas we
obtain the second class by dimensional reduction down to four dimensions, in
which there is a single class of invariants transforming in the next to minimal
unitary representation of $E_{7(7)}$.
