Background: The TheraP trial showed that LuPSMA improved PSA≥50% response rate (PSA50-RR), PSA-PFS, and radiographic PFS (rPFS) compared with cabazitaxel in mCRPC progressing after docetaxel. Study inclusion required high PSMA uptake (SUVmax≥20) and no lesions that were FDG+ and PSMA-. Here we report on PSMA PET and FDG PET as potential predictive and prognostic biomarkers. Methods: We prospectively analysed semi-automated quantitative PET parameters in centrally- collected ⁶⁸Ga-PSMA-11 PET and ¹⁸F-FDG PET in 200 eligible men. SUVmean ≥10 on PSMA PET was evaluated as a predictive biomarker for response to Lu-PSMA vs cabazitaxel. Metabolic tumor volume (MTV) ≥200mL on FDG PET was tested as a prognostic biomarker accounting for the randomly assigned treatment. Quantitative PET cut-offs were pre-specified from prior research (PMID:32140802). Responses were defined according to PSA50-RR (primary endpoint), PSA-PFS and rPFS. Binary and PFS endpoints were analyzed using logistic and Cox regression, respectively. Results: Very high PSMA uptake on PSMA PET (SUVmean≥10) was seen in 35/99 (35%) assigned LuPSMA and 30/101 (30%) assigned cabazitaxel. The odds of a response to LuPSMA vs. cabazitaxel were significantly higher for men with SUVmean≥10 (OR 12.2, 95%CI 3.4-59 vs. 2.2, 95%CI 1.1-4.5; p = 0.03). In men with SUVmean≥10, the PSA50-RR for LuPSMA vs. cabazitaxel were 32/35 (91%) vs. 14/30 (47%). In men with PSMA SUVmean < 10, the PSA50-RR were 33/64 (52%) vs. 23/71 (32%). High-volume metabolic disease on FDG PET (MTV ≥200mL) was seen in 30/99 (30%) assigned LuPSMA and 30/101 (30%) assigned cabazitaxel. The PSA50-RR in these men was 17/30 (57%) for LuPSMA vs. 6/30 (20%) for cabazitaxel. In comparison, the PSA50-RR for men with MTV < 200mL on FDG PET was 48/69 (70%) for LuPSMA vs. 31/71 (44%) for cabazitaxel. After accounting for treatment, the odds of a PSA50-response was lower among men with high MTV (OR 0.44; p = 0.01). The HR for PSA-PFS for LuPSMA vs cabazitaxel was 0.45 (95%CI 0.25-0.80) for SUVmean≥10 vs. 0.77 (95%CI 0.53-1.12) for SUVmean < 10 (p = 0.2). Findings were similar for rPFS. The HRs for high MTV on FDG PET adjusted for treatment were 1.44 (95%CI 1.03-2.02) for PSA-PFS (p = 0.03); and 1.79 (95%CI 1.28-2.52) for rPFS (p < 0.001). Conclusions: In men with mCRPC, PSMA SUVmean≥10 was predictive of a higher likelihood of favourable response to LuPSMA than cabazitaxel, whilst a high volume of disease on FDG PET was associated with a worse prognosis regardless of randomly assigned treatment. Clinical trial information: NCT03392428.