  In 1979, B. Shiffman conjectured that if f is an algebraically nondegenerate
holomorphic map of C into P^n and D_1,...,D_q are hypersurfaces in P^n in
general position, then the sum of the defects is at most n+1. This conjecture
was proved by M. Ru in 2004. In this paper, the Shiffman conjecture is proved
more generally in the case of slowly moving hypersurfaces in (weakly) general
position. Moreover, we introduce a truncation in the corresponding Second Main
Theorem, with an effective estimate on the truncation level, thus generalizing
a result of An-Phuong.
