This article introduces three areas of study: 1 telefunctioning; 2 a control method for producing telefunctioning; and 3 an analysis of human-robot interaction when telefunctioning governs the system behavior. Telefunctioning facilitates the maneuvering of loads by creating a perpetual sense of the load dynamics for the operator. Telefunctioning is defined as a robotic manipulation method in which the dynamic behaviors of the slave robot and the master robot are functions of each other; these functions are the designer’s choice and depend on the application. (In a subclass of telefunctioning currently referred to as telepresence, these functions are specified as “unity” so that the master and slave variables (e.g., position, velocity) are dynamically equal.) To produce telefunctioning, this work determines a minimum number of functions relating the robots’ variables, and then develops a control architecture which guarantees that the defined functions govern the dynamic behavior of the closed-loop system. The stability of the closed-loop system (i.e., master robot, slave robot, human, and the load being manipulated) is analyzed and sufficient conditions for stability are derived.