We study the Euclidean-signature supergravities that arise by compactifying D = 11 supergravity or type IIB supergravity on a torus that includes the time direction. We show that the usual T-duality relation between Type IIA and type IIB supergravities compactified on a spatial circle no longer holds if the reduction is performed on the time direction. Thus there are two inequivalent Euclidean-signature nine-dimensional maximal supergravities. They become equivalent upon further spatial compactification to D = 8. We also show that duality symmetries of Euclidean-signature supergravities allow the harmonic functions of any single-charge or multicharge instanton to be rescaled and shifted by constant factors. Combined with the usual diagonal dimensional reduction and oxidation procedures, this allows us to use the duality symmetries to map any single-charge or multi-charge p-brane soliton, or any intersection, into its near-horizon regime. Similar transformations can also be made on non-extremal p-branes. We also study the structures of duality multiplets of instanton and (D − 3)-brane solutions.