Thoracopagus conjoined twins were delivered at 31 weeks gestation by cesarean section. Although there was a single heart, the possibility of salvaging one twin only was contemplated. Echocardiography revealed an A-V canal and suspected transposition of the great vessels. To determine the possibility of surgery, cardiac catheterization was performed to rule out other congenital cardiac malformations incompatible with life, and also to delineate the exact anatomy of the great vessels of the heart. Unfortunately, complex congenital abnormalities were found, thus excluding the possibility of surgery. Newly delivered conjoined twins should be regarded as potentially correctable and should be promptly investigated while they are yet in good clinical condition.