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We consider the possible consistent truncation of N-extended supergravitiesto lower N' theories. The truncation, unlike the case of N-extended rigidtheories, is non trivial and only in some cases it is sufficient just to deletethe extra N-N' gravitino multiplets. We explore different cases (starting withN=8 down to N'\geq 2) where the reduction implies restrictions on the mattersector. We perform a detailed analysis of the interesting case N=2 \to N=1.This analysis finds applications in different contexts of superstring andM-theory dynamics.Comment: Version published on JHE

Supersymmetry reduction ofN-extended supergravities in four dimensions