A Boeing B737 was operating a scheduled flight from Darwin to Brisbane via route A464. The aircraft passed overhead Tindal at 1455, maintaining FL330, estimating the ATEGA waypoint (150 NM north-west of Mount Isa) at 1549. The aircraft was subsequently transferred from Brisbane ATC Sector 11K jurisdiction to Brisbane Sector 11 at 1515. Opposite direction traffic on A464 was a Boeing B747, operating a scheduled flight from Brisbane to Singapore. The aircraft passed overhead Mount Isa at 1430, maintaining FL310, estimating Tindal at 1613, and requesting a flight planned climb to FL350. The aircraft subsequently contacted Brisbane Sector 11 at ATEGA at 1525. The Sector 11 controller had calculated an estimated time of passing of 1538 for both aircraft and correctly notated both flight progress strips. The B747 was co-ordinated to Sector 11K with the current and planned cruising levels. However, at about 1528, Sector 11 cleared the B747 to climb to FL350. At 1535, the B747 reported maintaining FL350 but one minute later queried opposite direction traffic below. The Sector 11 controller immediately recognised that the prescribed separation standards had not been provided and the B747 had climbed through the level of the B737 about five minutes, or 80 NM, prior to the time of passing. A subsequent investigation found that the Sector 11 controller had been distracted by resolving a potential separation problem between two other aircraft within his area of responsibility. In addition, he had erroneously judged that all southbound traffic was below the B747, prior to issuing the climb clearance, although the relevant flight progress information available to him did not support this perception. A final opportunity to prevent the occurrence was lost when the crew of the B737 had apparently not recognised that the B747 had been cleared to climb through their level without adequate separation. The B737 had been on the same frequency as the B747 for some 10 mins prior to ATEGA.