中文摘要：

We give a complete classification of parallel hypersurfaces in the Euclidean ellipsoid Qn+1（c,d）.Moreover,we prove that a hypersurface in Qn+1（c,d） is totally umbilical,if and only if it is parallel.

英文摘要：

We give a complete classification of parallel hypersurfaces in the Euclidean ellipsoid Qn＋1 （e, d）. Moreover, we prove that a hypersurface in Qn＋1 （c, d） is totally umbilical, if and only if it is parallel.