  In this paper, we compare two cohomology groups associated to Shimura
varieties of PEL type, which are not proper over the base. One is the compactly
supported l-adic cohomology, and the other is the nearby cycle cohomology,
namely, the compactly supported cohomology of the nearby cycle complex for the
canonical integral model of the Shimura variety over Z_p. We prove that the
G(Q_p)-cuspidal part of these cohomology groups are the same, where G denotes
the reductive algebraic group naturally attached to the PEL datum. Some
applications to unitary Shimura varieties are also given.
