AbstractThis paper is part of a larger program, the investigation of the chord problem in three dimensional contact geometry. The main tool will be pseudoholomorphic strips in the symplectisation of a three dimensional contact manifold with two totally real submanifolds L0, L1 as boundary conditions. The submanifolds L0 and L1 do not intersect transversally. In this paper we will develop a nonlinear Fredholm theory that guarantees the existence of a family of embedded pseudoholomorphic strips near a given one with suitable properties. © 2003 Wiley Periodicals, Inc.