A hybrid simulation is carried out to study the evolution of magnetic field rotations in rotational discontinuities (RDs) and large-amplitude Alfv¿n wave trains (AWTs) whose initial field rotation angle |Δ&PHgr;|>180¿. For a given initial half width D, the RDs or AWTs lose a multiple of ¿360¿ field rotation at a critical time, until a smallest rotation angle |Δ&PHgr;|0.1, and decreases with decreasing shock normal angle &thgr;Bn. At t180¿ for a given transient convection time at the dayside magnetopause and minimum widths of AWTs per 360¿ field rotation in the solar wind. ¿ 2000 American Geophysical Union