A cryosurgical instrument includes a feed line for conveying fluid into an expansion chamber. The feed line has a capillary line section that terminates in the expansion chamber and forms an aperture for the fluid to undergo the Joule-Thomson effect. The flow cross-section of the feed line decreases in at least one transition section of the feed line in the form of a funnel. Following each transition section there preferably follows a step section, in which latter section the flow cross-section is preferably largely constant. The last step section is preferably formed by the capillary line section. Due to the acceleration of the fluid in the transition sections and the abating of pressure fluctuations in the capillary tube section and, optionally in the additional step sections, the expansion range in the expansion chamber is increased, without impeding the backflow of the expanded gas out of the expansion chamber.
