British Military Administration (BMA)
The BMA took charge of Brunei's postal service on 17 December 1945 and treated all four British Borneo teritories as one unit (as also had the Japanese). Sarawak stamps of the 1934-41 issue and North Borneo 1939 issue were overprinted "BMA".
None of the Brunei stamps were overprinted primarily because of insufficient stock from previous issue - this is likely because the little number of remaining 1924-37 Brunei stamps might have been used up for Japanese overprints. Also both North Borneo and Sarawak stamps were sufficient enough to provide for postal need in Brunei during the BMA administration. The use of BMA stamps ceased with the reappearance of new Brunei issues on 2 January 1947.
Three-line postmark supplied by Straits Times, Singapore - Kuala Belait
Very few postmarks were used during BMA and mainly from the two main towns - Brunei and Kuala Belait. I'm not sure about postal services in Tutong and Temburong during BMA, but both Muara and Seria were not opened until 1948 and 1951 respectively.
Two varieties of postmarks were produced: (a) A three-line postmark provided by the Straits Times in Singapore; and (b) An Australian pattern cds. Both varieties were available for both towns. Two further varieties found for the three-line postmarks for both Brunei and Kuala Belait.
Australian pattern cds - Kuala Belait
Australian pattern cds - Brunei
More about Brunei Stamps.
Related post: Brunei RAF Survey Flight 1930-31