  We introduce the notion of finite slope families to encode the local
properties of the p-adic families of Galois representations appearing in the
work of Harris, Lan, Taylor and Thorne on the construction of Galois
representations for (non-self dual) regular algebraic cuspidal automorphic
representations of GL(n) over CM fields. Our main result is to prove the
analytic continuation of semi-stable (and crystalline) periods for such
families.
