We describe the growth of InAIN/GaN heterostructures by rf-plasma molecular beam epitaxy. Due to the weak In-N bond, the MAIN growth temperature must be below about 460 degrees C for In to incorporate reliably into the film. Thus far, a thin AIN spacer layer has been required to form a low resistance two dimensional electron gas (2DEG) at the InAIN/GaN interface. The thin AIN barrier is believed to reduce alloy scattering of carriers in the 2DEG. The best HEMT material with an MAIN barrier and a thin AIN spacer layer has a sheet resistance of 980 Omega/rectangle with a sheet electron density of 1.96 X 10(13) cm(-2). (c) 2005 American Vacuum Society.