This paper describes the occurance of and presents a solution to shaft failures caused by an unstable asynchronous critical speed, which occurred on a two-part high-speed shaft coupled to a gearbox. The two-part shaft exhibited a first bending synchronous critical speed just below or in the lower portion of the operating speed range of the gearbox. It also exhibited a re-exitation of the same critical speed at a frequency below the rotational speed in the upper portion of the operating speed range. This subsynchronous re-exitation was attributed to the friction generated at the pilot/spline interfaces between the gearbox input shaft and the shaft coupled to it. Because the gearbox operating speed is well defined and limited, the solution to the problem was to raise the first bending frequency beyond the operating range, by redesigning the shafts to increase stiffness, thus eliminating the critical frequency and its re-exitation as a problem.