Critical speed tests were performed on the Power Take Off shaft subsystem of the Grumman X-29A advanced technology demonstration aircraft. Test speeds up to 20,000 rpm were run to insure stable operation up to the maximum installed overspeed of 17,250 rpm. The subsystem was instrumented with proximity probes and accelerometers to measure shaft displacement and vibration. This paper will show that unprocessed data from proximity probes and accelerometers does not reliably indicate the location of a critical speed, and it will outline a method for processing this type data to accurately determine the critical speed. An example of reverse precession, as well as the effects of unbalance on critical speed, will be presented.