Several newly proposed superconducting linacs are designed to use TESLA technology operating CW rather than pulsed for which the system was developed. It must therefore be demonstrated that CW operation is feasible. Here we describe a series of CW tests with the TTF-III power coupler to determine the average power limit. These tests were performed on a coupler test stand both at room temperature at the FZ Rossendorf and under cryogenic operating conditions in BESSY’s HOBICAT[1] facility. An extrapolation of the measurements suggests that the coupler can handle 5 kW CW standing wave. It was also demonstrated that even higher power levels are feasible if the cooling of the inner conductor is modified.