  We consider the possible consistent truncation of N-extended supergravities
to lower N' theories. The truncation, unlike the case of N-extended rigid
theories, is non trivial and only in some cases it is sufficient just to delete
the extra N-N' gravitino multiplets. We explore different cases (starting with
N=8 down to N'\geq 2) where the reduction implies restrictions on the matter
sector. We perform a detailed analysis of the interesting case N=2 \to N=1.
This analysis finds applications in different contexts of superstring and
M-theory dynamics.
