A titanium-aluminide turbine wheel (120, 220, 320, 420) is joined to the end of a shaft (110, 210, 310, 410) by utilizing a titanium surface on the end of the shaft to be joined to the wheel, and electron-beam welding the wheel onto the titanium surface on the shaft. A steel shaft (110, 310, 410) can have a titanium-containing end piece (130, 330, 430) mechanically joined (by brazing, bonding, or welding) to the end of the shaft, and the end piece can be directly electron-beam welded to the wheel. Alternatively, the shaft (210) can be formed as a titanium member and the end (212) of the shaft can be directly electron-beam welded to the wheel (220). In another embodiment, a ferrous end piece (330) is mechanically joined to the titanium-aluminide turbine wheel (320) and then the end piece is directly electron-beam welded to the end of a steel shaft (310). Alternatively, a silver-titanium alloy member (430) is sandwiched between the wheel (420) and a steel shaft (410) and is melted to join the parts together.