Histopathological proven metastatic castration resistant prostate cancer. Castrationresistant disease is defined as a serum testosterone level of 50 nanogram per deciliter or lower (≤1.7 nanomol per liter) after bilateral orchiectomy or during maintenance treatment consisting of androgen-ablation therapy with a luteinizing hormone-releasing hormone agonist.

Evidence of progressive disease, defined as 1 or more Prostate Cancer Work Grouping 3 (PCWG3) criteria: - PSA level ≥ 1 ng/mL that has increased on at least 2 successive occasions at least 1 week apart

Progression as defined by RECIST 1.1 with PCGW3 modifications

Progression after at least one line of chemotherapy and/or one line of nonsteroidal antiandrogen (NSAA).

No active anti-tumor therapy, except for androgen deprivation therapy in combination with at least one androgen receptor-targeted agent

Willing and able to undergo 2 cycles of 225Ac-PSMA I\&T therapy and 3 PET-MRI scans in 16 weeks and comply with protocol

Signed and dated written informed consent by the patient (or legal representative) prior to any study-specific procedures.

Age ≥ 18 years.

Eastern Cooperative Oncology Group (ECOG) performance-status score 0-2.

Use of highly effective methods of contraception (female partners of male participants)

During the trial and 6 months after completion of the study or willing to practice sexual abstinence.

Concurrent severe illness or clinically relevant trauma within 2 weeks before the administration of the investigational product that might preclude study completion or interfere with study results

Serum hemoglobin ≤ 6.2 mmol/L, total white blood cell (WBC) count ≤ 3.5·109/L, absolute neutrophil count ≤ 1.5·109/L, platelet count ≤ 100·109/L, serum creatinine concentration ≥ 150 umol/L (≥ 1.7 mg/dL), serum albumin \<30 g/L, bilirubin ≥ 1.5 x upper limit normal (ULN), aspartate transaminase (ASAT) ≥ 3 x ULN and alanine aminotransferase (ALAT) ≥ 3 x ULN (or bilirubin ≥ 3 x ULN, ASAT ≥ 5 x ULN and ALAT ≥ 5 x ULN in the case of pre-existing liver metastases at baseline)

Concurrent bladder outflow obstruction or unmanageable urinary incontinence

Known or expected hypersensitivity to Gallium-68, Actinium-225, PSMA I\&T, or any excipient present in 225Ac/68Ga-PSMA I\&T

Prior administration of a radiopharmaceutical within a period corresponding to 8 halflives of the radionuclide used on such radiopharmaceutical

Prior treatment with any radionuclide therapy

History of somatic or psychiatric disease/condition that may interfere with the objectives and assessments of the study

Central nervous system (CNS) metastases, leptomeningeal disease, or spinal cord compression

Radiation therapy within 4 weeks of first dose (or local or focal radiotherapy within 2 weeks of first dose)

Male subjects unwilling to abstain from donating sperm during treatment and for an additional 6 months after the last dose