  We classify non-dilatonic NS-NS type II supergravity backgrounds admitting a
consistent absolute parallelism. They are all given by parallelised Lie groups
admitting scalar flat bi-invariant lorentzian metrics. There are seven
different classes, some of them containing moduli. For each class we determine
the amount of supersymmetry which is preserved: there are examples with 16, 18,
20, 22, 24, 28 and 32 supersymmetries.
