The pilot of the first aircraft in the sequence, from Australian Airlines, requested direct track from over Devonport to Hobart on the 320 radial. On co-ord with Hobart Air Traffic Control approval given for this and a second aircraft, this one from Ansett Airlines, to also track direct. The Sector 3 controller passed the clearance to the first aircraft but forgot to pass it to the second one. The second aircraft arrived in the Hobart area on the 301 radial, which was the original planned route, instead of the 320 radial as expected. No loss of separation occurred.