  We apply the theory of families of (phi,Gamma)-modules to trianguline
families as defined by Chenevier. This yields a new definition of Kisin's
finite slope subspace as well as higher dimensional analogues. Especially we
show that these finite slope spaces contain eigenvarieties for unitary groups
as closed subspaces. This implies that the representations arising from
overconvergent p-adic automorphic forms on certain unitary groups are
trianguline when restricted to the local Galois group.
