Background: We previously reported that in men with mCRPC progressing after docetaxel randomly assigned LuPSMA vs. cabazitaxel (Lancet 2021), those assigned LuPSMA has significant improvements in PSA response rate (66% vs. 37%), RECIST response rate (49% vs. 24%), progression-free survival (HR 0.63), less G3-4 toxicities (33% vs. 53%) and better patient-reported outcomes. We now report the secondary endpoint of overall survival (OS) with mature follow-up, for trial participants, and also those initially excluded because of low PSMA-expression or discordant disease on imaging with PSMA-PET and FDG-PET. Methods: Eligibility for the TheraP trial required mCRPC progressing after docetaxel, PET imaging with ⁶⁸Ga-PSMA-11 that showed high PSMA-expression (at least one site with SUVmax≥20), and ¹⁸F-FDG demonstrating no sites of disease of FDG-positive and PSMA-negative (discordant disease). Participants were randomly assigned treatment with LuPSMA (8.5-6GBq every 6 weeks, maximum 6 cycles) vs cabazitaxel (20mg/m² every 3 weeks, maximum 10 cycles). OS was analyzed by intention-to-treat and summarized by restricted mean survival time (RMST) to account for non-proportional hazards. Results: 291 patients were screened from 6 Feb 2018 to 3 Sep 2019: 200 were eligible and randomly assigned LuPSMA (99) or cabazitaxel (101); 80 of 291 (27%) registered after initial eligibility were excluded after PSMA/FDG-PET(51 SUVmax < 20, 29 discordant), with follow-up available in 61 of the 80 (76%). After a median follow-up time of 36 months (data cut-off 31 Dec 2021), death was reported in 70/101 assigned cabazitaxel, 77/99 assigned LuPSMA, and 55/61 excluded after PSMA/FDG-PET. Subsequent treatments among those assigned cabazitaxel included cabazitaxel in 21, and LuPSMA in 20; and among those assigned LuPSMA included additional LuPSMA in 5, and cabazitaxel in 32. Overall survival was similar in those randomly assigned LuPSMA versus cabazitaxel (RMST to 36 months was 19.1 vs. 19.6 months, difference -0.5, 95% CI -3.7 to + 2.7). No additional safety signals were identified with longer follow-up. Among 61 men excluded by imaging with PSMA/FDG-PET before randomisation, RMST to 36 months was 11.0 months (95% CI 9.0 to 13.1), following treatment that included cabazitaxel in 29 (48%) and LuPSMA in 3 (5%). Conclusions: LuPSMA is a suitable option for men with mCRPC progressing after docetaxel, with lower adverse events, higher response rates, improved patient-reported outcomes, and similar OS compared with cabazitaxel. Median survival was considerably shorter for patients excluded on PSMA/FDG-PET due to either low PSMA expression or FDG-discordant disease who would otherwise be eligible for LuPSMA. Clinical trial information: NCT03392428.