The invention proposes a cryosurgical instrument and its accessory system operating on the base of a refrigerant evaporation. The invention comprises combination of some technical solutions. Flow in a central lumen of the cryosurgical instrument has oscillating character; the refrigerant is provided on the internal surface of the distal cryotip in the form of separated portions. 2. The internal surface of the distal cryotip of the cryosurgical instrument is covered by a porous coating, which soaks completely one portion of the refrigerant. 3. Vapors obtained as a result of the refrigerant boiling on the porous coating of the cryotip are removed through the central lumen into the atmosphere. Combination of these technical solutions allows to construct a safely cryosurgical instrument with high freezing power and small outer diameter. The proposed cryosurgical instrument may be designed as a flexible cryocatheter or as a rigid cryoprobe.