The functional optimization of the composition of radiopharmaceutical pairs based on the prostatespecific membrane antigen (PSMA) for the radionuclide theranostics of castration-resistant prostate cancer was carried out. The analysis of radiation-physical and dosimetric characteristics of 9 radionuclides for diagnostic components of theranostic pairs and 6 radionuclides for therapeutic components is carried out. It was shown that positron-emitting radionuclides 18F and 68Ga should be considered optimal for the diagnosis and monitoring of the effectiveness of theranostics, and 177Lu beta-emitting radionuclide and 225Ac alphabeta-emitting radionuclide should be considered as the radionuclide therapy. The values of the total and organ radiation risks of secondary radiation-induced cancers in patients who have completed several courses of theranostics are calculated. It is shown that for 2 teranostic pairs based on 177Lu‑PSMA the radiation risk is higher than significant, while for 2 teranostic pairs based on 225Ac the risk falls within the range of a significant level. The calculated radiological criteria for discharge of patients after a course of theranostics from nuclear medicine departments show the fundamental possibility of performing an outpatient treatment regimen using any of the 4 considered theranostic pairs.