  In this paper we study the slope stratification on the good reduction of the
type C family Shimura varieties. We show that there is an open dense subset $U$
of the moduli space such that any point in $U$ can be deformed to a point with
a given lower {\it admissible} Newton polygon. For the Siegel moduli spaces,
this is obtained by F. Oort which plays an important role in his proof of the
strong Grothendieck conjecture concerning the slope stratification. We also
investigate the $p$-divisible groups and their isogeny classes arising from the
abelian varieties in question.
