A system for use in conducting coronary surgery permits coronary surgery on a beating heart while maintaining cardiac output unabated and uninterrupted. Circumflex coronary artery surgery can be performed using the system. The system includes a first device for engaging and repositioning the beating heart to a displaced position, and is capable of maintaining the heart in the displaced position to perform a surgical procedures. The system includes a second device adapted to engage a portion of the heart to immobilize that portion for conducting a surgical procedure in the immobilized location, while the remainder of the heart continues to beat. Both first and second devices may be adapted to be fixed to a relatively stationary object, such as a frame, which may be a sternal retractor.