Teleoperation continues to be a primary control mode in robotics applications, particularly for robots with complex hands. This paper details a novel method of teleoperation of complex anthropomorphic robotic hands: converting the myoelectric signal (generated by the operator's muscles during movement) into robot commands replicating the motion. Myoelectric prosthetic hands have used this user interface for over two decades; however, the feasibility of using this approach for commanding more than one degree-of-freedom, as in the pincher type grip in current myoelectric hands, has been in question. The research described in this paper addresses myoelectric control of NASA/Johnson Space Center's sixteen degree-of-freedom Utah/MIT Dextrous Hand for two grasping (key and chuck) options and three thumb motions (abduction, extension, and flexion). We discuss myoelectric signal processing approaches, data collection apparatus, and a realtime teleoperation implementation. We also present results in realtime discrimination of key and chuck grasps and offline discrimination of thumb motions. Our results include a 90% correct grasp selection rate and an 87% correct thumb motion selection, both using the myoelectric spectrum.