Canberra Approach received coordination from Sydney Flight Information Service(2)(FIS) concerning VH-OFF estimating Shelleys at 0541 and cruising at 10,000 feet. Subsequently no call was received from the aircraft, but another aircraft which was conducting training at Canberra advised that VH-OFF was attempting to call Canberra. Instructions were passed to VH-OFF through this other aircraft that clearance through Canberra control area would not be available unless satisfactory two way communications could be established. Shortly after this a code 7600 transponder squawk (Radio Failure) was observed on radar over Lake George inside controlled airspace. VH-OFF was instructed by FIS2 to call Canberra Approach but the aircraft did not establish contact and was instructed through FIS2 to leave controlled airspace. The pilot of VH-OFF reported that he was able to communicate with other aircraft on Canberra Approach frequency, and Canberra Approach was the only station not reading VH-OFF. The pilot said that he had expected to establish communications with Canberra Approach, and had decided initially to continue as per flight plan. He was then instructed to leave controlled airspace tracking 270 degrees, and acknowledged this with two clicks of the microphone button. He advised FIS2 that he was able to descend clear of controlled airspace and remain visually clear of high terrain. No further communications problems were experienced for the remainder of the flight.