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Let p>2 be a prime and let X be a compactified PEL Shimura variety of type(A) or (C) such that p is an unramified prime for the PEL datum. Using thegeometric approach of Andreatta, Iovita, Pilloni, and Stevens we define thenotion of families of overconvergent locally analytic p-adic modular forms ofIwahoric level for X. We show that the system of eigenvalues of any finiteslope cuspidal eigenform of Iwahoric level can be deformed to a family ofsystems of eigenvalues living over an open subset of the weight space. To provethese results, we actually construct eigenvarieties of the expected dimensionthat parametrize systems of eigenvalues appearing in the space of families ofcuspidal forms.

Eigenvarieties for cuspforms over PEL type Shimura varieties with dense ordinary locus