For the limiting cases of conical flow about delta wings and time dependent 2-D development of the wake behind the trailing edge of wings a new second-order panel method is described. It is demonstrated that the panel method is stable for the mixed design/analysis boundary conditions characterizing both problems. The method for following 2-D vortex sheet motion includes an adaptive curvature-dependent panel scheme and a concept for doubly-branched spiralling vortices, which enables the motion of vortex sheets of complicated shape to be followed up to large downstream distances. Conical flow results are presented for different angles of attack and for different cross-sectional shapes. Vortex sheet roll-up results are presented for the wake behind a flat delta wing.