  We show that, under suitable assumptions, the systems of Hecke eigenvalues
arising from (mod p) modular forms of PEL-type associated to an algebraic group
G of type A or C coincide with the Hecke eigensystems arising from (mod p)
algebraic modular forms for an inner form of G. We treat explicitly the case of
unitary groups, and we give in this case an asymptotic formula for the number
of eigensystems. The paper generalizes results of J-P. Serre for GL(2) and A.
Ghitza for GSp(2g).
