The analysis presented shows that the classical model of non-linear magnetic field line reconnection changes considerably in the presence of sheared magnetic fields and/or high tangential plasma flow components. This shear excites large amplitude Alfvén waves on both sides of the reconnection layer where the magnetic field is rotated to a common direction within the layer. In addition two slow shock (or rarefaction) waves within the reconnection layer are necessary to account for the remaining shear in plasma flow. The detailed structures of such reconnection layers with implications for magnetopause reconnection events are discussed.