  The recent mathematical literature introduces generalised geometries which
are defined by a reduction from the structure group $SO(d,d)$ of the vector
bundle $T^d\oplus T^{d*}$ to a special subgroup. In this article we show that
compactification of IIB superstring vacua on 7-manifolds with two covariantly
constant spinors leads to a generalised $G_2$-structure associated with a
reduction from SO(7,7) to $G_2\times G_2$. We also consider compactifications
on 6-manifolds where analogously we obtain a generalised SU(3)-structure
associated with $SU(3)\times SU(3)$, and show how these relate to generalised
$G_2$-structures.
