The patient population for a phase Ⅱ clinical trial sometimes consists of multiple subgroups categorized by different prognostic factors such as age,disease stage,etc.Response rates across such subgroups often are heterogeneous;i.e.,the therapy under study may be inefficacious in some groups but efficacious in others.In this article,we propose a two-stage testing procedure consisting of futility tests and efficacy tests.The futility test is performed first within each subgroup.If there is strong evidence that the therapy is inefficacious in some subgroups,these subgroups are excluded from further consideration.The test then is performed across only the remaining subgroups.We carefully define and compute the Type Ⅰ error rate and powers under various alternative hypotheses.Our numerical studies show that with proper designs,the addition of futility tests causes little loss of power under the alternative hypothesis that the study therapy is efficacious in all subgroups.Simultaneously,the proposed testing procedure detects inefficacious subgroups with a moderate or high probability when true response rates in these subgroups are low.Finally,we present an application to a Childrens Oncology Group phase Ⅱ clinical trial in relapsed neuroblastoma patients.