  This paper is a continuation of our paper math.AG/0006222. We study the
reduction of certain PEL Shimura varieties with parahoric level structure at
primes p at which the group that defines the Shimura variety ramifies. We
describe "good" $p$-adic integral models of these Shimura varieties and study
their 'etale local structure. In particular, we exhibit a stratification of
their (singular) special fibers and give a partial calculation of the sheaf of
nearby cycles.
