In many biological and other scientific applications,prediction variables are naturally grouped.For example,in biological applications,assayed genes or proteins are grouped by biological roles or biological pathways.When studying the dependence of survival outcome on these grouped prediction variables,it is desirable to select variables at both the group level and the variable-specific level.In this article,we develop a new method to handle the group variable selection in the Cox proportional hazards model.Our method not only effectively removes unimportant groups,but also maintains the flexibility of selecting variables within the identified groups.We also show that the new method offers the potential for achieving the asymptotic oracle property as in Fan and Li (2001,2002).