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Given a complex manifold S, we introduce for each complex manifold X at-structure on the bounded derived category of C-constructible complexes ofO_S-modules on X x S. We prove that the de Rham complex of a holonomicD_{XxS/S}-module which is O_S-flat as well as its dual object is perverserelatively to this t-structure. This result applies to mixed twistor D-modules.

On the de Rham complex of mixed twistor D-modules