• Males ≥ 18 years of age

• Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 assessed within 7 days of study treatment initiation

• Histologically or cytologically confirmed adenocarcinoma of prostate (Patients with small cell carcinoma of the prostate may be included)

• Metastatic disease documented by at least one lesion on bone scan or abdominal/pelvic/chest computed tomography (CT) or magnetic resonance imaging (MRI) scan assessed by investigator. Patients without bone metastasis must have measurable lesions in extra-pelvic lymph nodes or in soft-tissues as defined by RECIST 1.1 criteria

• Confirmed progression mCRPC despite ongoing androgen deprivation with serum testosterone \< 50ng/dl (1.7nM) within 3 months prior to screening. Progression is defined by the presence of at least one of the following criteria :

‣ PSA progression using local laboratory values as defined by a minimum of 2 consecutive rising PSA levels with an interval of ≥1 week between each assessment where the PSA value at screening should be ≥1 ng/mL

⁃ Radiographic disease progression in bone based on PCWG3 criteria defined as the appearance of 2 or more new bone lesions on bone scan, with or without PSA progression

⁃ Radiographic disease progression in extra-pelvic lymph nodes based or soft-tissues on RECIST1.1 criteria with or without PSA progression

• PSMA positive metastatic lesions on \[68Ga\]-PSMA-PET/CT without PSMA negative lesion (The presence of PSMA-positive lesions is defined as \[68Ga\]-PSMA-11 uptake greater than that of liver parenchyma in one or more metastatic lesions of any size in any organ system. The presence of PSMA-negative lesions is defined as PSMA uptake equal to or lower than that of liver parenchyma in any lymph node with a short axis of at least 2.5 cm, in any metastatic solid-organ lesions with a short axis of at least 1.0 cm, or in any metastatic bone lesion with a soft-tissue component of at least 1.0 cm in the short axis. Patients with any PSMA negative metastatic lesion meeting these criteria are ineligible).

• Participants must have been previously treated with at least 4 consecutive cycles of \[177Lu\]Lu-PSMA with no evidence of progression during this first course of treatment (including radiological, clinical but also PSA progression). (Patients with a radiological or clinical progressive disease during the first 120 days after the last cycle of the first course of \[177Lu\]Lu-PSMA are not eligible. PSA progression is defined by a ≥ 25% increase in PSA and an absolute increase of 2 ng/mL or more from the NADIR and confirmed by a second consecutive value obtained 3 or more weeks later)

• Participants must have been previously treated with at least one ARSI - Androgen Receptor Signaling Inhibitors - (including enzalutamide, apalutamide, abiraterone or darolutamide) initiated for mCSPC, nmCRPC or mCRPC. (ARSI may be also administered together with \[177Lu\]Lu-PSMA-617 provided that the patient has not received an identical ARSI in the past and that this ARSI was initiated at least 15 days before the first cycle of \[177Lu\]Lu-PSMA-617 and less than 2 months ago. The ARSI administrated in association with LuPSMA should not be considered as a prior therapy. A previous ARSI treatment is mandatory for patient eligibility)

• Patients must have been previously treated with at least one taxane based chemotherapy (with docetaxel or cabazitaxel)

• Patients must have been treated with at least one course of taxane based chemotherapy (docetaxel or cabazitaxel) after the first course of \[177Lu\]Lu-PSMA therapy. (Patients treated with PARP inhibitors, or more than one course of chemotherapy between the first 117LuPSMA course and screening are also eligible).

• Be abstinent from heterosexual intercourse OR must agree to use contraception unless confirmed to be azoospermic (vasectomized or secondary medical cause) until 98 days (14 weeks) post-treatment.

• Adequate organ functions :

‣ Bone marrow reserve :

• ANC ≥ 1.5 X 109/L

∙ Platelets ≥ 100 X 109/L

∙ Hemoglobin ≥ 10 g/dL

⁃ Hepatic :

• Total bilirubin ≤ 2 x ULN. For patients with known Gilbert's syndrome ≤ 3 x ULN.

∙ Alanine aminotransferase (ALT) or aspartate aminotransferase (AST) ≤3 x ULN

⁃ Renal :

• Clearance ≥40 ml/mn

• Patients must have signed informed consent prior to participating in any study related procedures

• Willing and able to comply with the protocol, including follow-up visits and examinations

• Patients have to be affiliated to the French social security system