Images of static vascular maps (B), which were taken at different phases of the cardiac cycle and/or the respiratory cycle and were archived in a memory (6), are superimposed on a current image (A) of a catheter (2, 8) in the vascular system (9). In the method, a defined section of a map image (B) around the estimated actual position of the catheter is selected and is displayed superimposed on the current image (A) on a monitor (10). The map image (B) used for this is preferably selected by an electrocardiogram to match the particular cardiac cycle. The position of the catheter relative to the map image (B) is estimated using a distance image (D).
