  The name of Oka principle, or Oka-Grauert principle, is traditionally used to
refer to the holomorphic incarnation of the homotopy principle: on a Stein
space, every problem that can be solved in the continuous category, can be
solved in the holomorphic category as well. In this note, we begin the study of
the same kind of questions on a Levi-flat manifold; more precisely, we try to
obtain a classification of CR-bundles on a semiholomorphic foliation of type
(n, 1). Our investigation should only be considered a preliminary exploration,
as it deals only with some particular cases, either in terms of regularity or
bidegree of the bundle, and partial results.
