This dissertation introduces a novel method of teleoperation of complex anthropomorphic robotic hands: converting the myoelectric signal generated by an operator's muscles during movement into robot commands replicating the motion. This teleoperation scenario is, in a sense, the limiting case of myoelectric prosthetic hand control. This project contributes to implementation of a practical myoelectric teleoperation system and improved prosthetic hand control by analyzing the myoelectric spectrum's variation during thumb motions. The investigation applies a new spectral estimation approach, Thomson's multiple window method (MWM), to the myoelectric signal. The MWM estimate has much lower bias and variance than traditional periodogram estimates, making it a better candidate to compute motion classification features. The MWM is also less sensitive to motion artifact than autoregressive methods. Extending Thomson's MWM into a time-frequency analysis tool analogous to the short-time Fourier transform, here called the short-time Thomson transform, shows that the myoelectric signal may be more stationary than previously thought. This project includes development of a unique myoelectric data collection system (MDCS) and a myoelectric teleoperation demonstration system (MTDS). The MDCS allows simultaneous measurement of 16 hand joint motions and 8 myoelectric signals. This capability enables close alignment of myoelectric signatures in time based on the hand motions and a search for motion-specific temporal characteristics in the myoelectric signal. While this study yields little evidence of motion-specific temporal consistency, it shows promising motion-specific spectral consistency. Spectral analysis proves less sensitive to alignment uncertainties than temporal analysis. An evaluation of five techniques for finding a motion's starting point in the myoelectric signal, a major implementation concern, suggests that we not pursue alignment-sensitive myoelectric control algorithms. Finally, the MTDS is used to demonstrate myoelectric control of chuck and key grasp motions of NASA/JSC's Utah/MIT Dextrous Hand, realtime, with 90% accuracy. The demonstration uses the time-varying myoelectric spectrum estimated with short-time Fourier transforms; however, this project lays the foundation for using the superior short-time Thomson transforms in this application.