  The main goal of this paper is to generalize Serre-Tate theory of "ordinary"
local moduli to Shimura varieties of PEL type. To this end we develop a
generalized notion of ordinariness, we prove a number of basic results about
this, and we study the formal deformations of ordinary objects. In general, the
formal deformation spaces get a new "group-like" structure that we call a
"cascade". Further the paper contains some results on the Ekedahl-Oort
stratification of PEL moduli spaces, and an application of our results to the
study of congruence relations.
