Let F be a foliation in a closed 3-manifold with negatively curved fundamental group and suppose that F is almost trans-
verse to a quasigeodesic pseudo-Anosov °ow. We show that the leaves of the foliation in the universal cover extend continuously
to the sphere at in¯nity; therefore the limit sets of the leaves are continuous images of the circle. One important corollary is that if
F is a Reebless, ¯nite depth foliation in a hyperbolic 3-manifold, then it has the continuous extension property. Such ¯nite depth
foliations exist whenever the second Betti number is non zero. The result also applies to other classes of foliations, including a large
class of foliations where all leaves are dense, and in¯nitely many examples with one sided branching. One extremely useful tool is
a detailed understanding of the topological structure and asymptotic properties of the 1-dimensional foliations in the leaves of e F induced by the stable and unstable foliations of the °ow.