Summary: A new class of six-dimensional asymmetric orientifolds is considered where the orientifold operation is combined with T-duality. The models are supersymmetric in the bulk, but the cancellation of the tadpoles requires the introduction of brane configurations that break supersymmetry. These can be described by D7-brane-antibrane pairs, non-BPS D8-branes or D9-brane-antibrane pairs. The transition between these different configurations and their stability is analysed in detail.