This single-arm phase II trial (ACTRN12620000918921) evaluated the clinical activity of tremelimumab (10 mg/kg intravenously every 4 weeks for 6 cycles) in advanced cancers with a high tumour mutational burden (TMB), defined as TMB > 10 mutations/megabase (mut/Mb) on standard platforms (TSO500 panel, F1CDx), or >20 mut/Mb on the TST170 panel. The primary objective was 6-month progression-free survival rate (PFS6) by iRECIST. Secondary objectives included objective response; the ratio of time to progression (TTP) on study to TTP on prior therapy (TTP2:TTP1); overall survival (OS); and safety. After minimum followup of 12 months, the PFS6 was 6% (95% CI 0-24%), with a median PFS and OS of 1.9 (95% CI 1.4-2.8) and 6.3 (2.8-10.3) months, respectively. Amongst 19 evaluable patients, two partial responses occurred in an endometrial adenocarcinoma and an undifferentiated pleomorphic sarcoma, maintained for 3.8 and 15.9 months respectively, both with TMB >20 mut/Mb. Adverse events were experienced by 19 patients (90%), with 15 patients (72%) experiencing grade 3-5 adverse events. Seven tremelimumab-related serious adverse events (grade 2-3) occurred in 5 patients. While the primary PFS6 endpoint was not met, there were two durable objective responses in rare cancers and a favourable change in disease trajectory for an additional five patients based on TTP ratio 1.3.