A catheter system for ablating biological material, in particular for ablating muscle tissue of the human or animal heart, the catheter system comprising a catheter device (20, 60a, 60b, 90) and a measurement device (43, 44, 50), the catheter device (20, 60a, 60b, 90) comprising a longitudinal structure (62, 63, 65); a cryo-applicator (53, 61, 66) for ablating the biological material, wherein the applicator (53, 61, 66) is installed at the longitudinal structure (62, 63, 65); a first electrode (23, 23a, 23i) being attached to the applicator (53, 61, 66) or to the longitudinal structure (62, 63, 65); a second electrode (46, 46a, 46b) being attached to the longitudinal structure (62, 63, 65); an interface (47a, 47b, 48, 49) being connected directly or indirectly to the longitudinal structure (62, 63, 65); a first lead (22, 22a, 22i) electrically connecting the first electrode (23, 23a, 23i) with the interface (47a, 47b, 48, 49); a second lead (45a, 45b) electrically connecting the second electrode (46, 46a, 46b) with the interface; wherein the interface (47a, 47b, 48, 49) is configured for electrically connecting the first lead (22, 22a) and the second lead (45a, 45b) with the measurement device (43, 44, 50) for electrically stimulating the first electrode (23, 23a, 23i) and the second electrode (46, 46a, 46b) and for detecting an electric quantity being associated with an electric response of an biological material being located in between the two stimulated electrodes (23, 23a, 23i; 46, 46a, 46b); the measurement device (43, 44, 50) comprising a stimulating unit for electrically stimulating the first electrode (23, 23a, 23i) and the second electrode (46, 46a, 46b);:PS:mp a detecting unit for detecting an electric quantity received from the first electrode and the second electrode; and a computing unit for determining, based on the detected electric quantity, an electric impedance of the biological material being located in between the two stimulated electrodes (23, 23a, 23i; 46, 46a, 46b); wherein the stimulating unit is configured for stimulating the first electrode (23, 23a, 23i) and the second electrode (46, 46a, 46b) with an adjustable predetermined electric current amplitude in such a manner that with a first level of the adjustable predetermined electric current amplitude a wall contact between (a) the first electrode and/or the second electrode on the one hand and (b) tissue on the other hand is detected and with a second level of the adjustable predetermined electric current amplitude a formation of ice within the biological material being located in between the two stimulated electrodes is recognized, wherein the second level is below 0.01 mA, wherein the second level is smaller than the first level. a longitudinal structure (62, 63, 65); a cryo-applicator (53, 61, 66) for ablating the biological material, wherein the applicator (53, 61, 66) is installed at the longitudinal structure (62, 63, 65); a first electrode (23, 23a, 23i) being attached to the applicator (53, 61, 66) or to the longitudinal structure (62, 63, 65); a second electrode (46, 46a, 46b) being attached to the longitudinal structure (62, 63, 65); an interface (47a, 47b, 48, 49) being connected directly or indirectly to the longitudinal structure (62, 63, 65); a first lead (22, 22a, 22i) electrically connecting the first electrode (23, 23a, 23i) with the interface (47a, 47b, 48, 49); a second lead (45a, 45b) electrically connecting the second electrode (46, 46a, 46b) with the interface; a stimulating unit for electrically stimulating the first electrode (23, 23a, 23i) and the second electrode (46, 46a, 46b);:PS:mp a detecting unit for detecting an electric quantity received from the first electrode and the second electrode; and a computing unit for determining, based on the detected electric quantity, an electric impedance of the biological material being located in between the two stimulated electrodes (23, 23a, 23i; 46, 46a, 46b); wherein the stimulating unit is configured for stimulating the first electrode (23, 23a, 23i) and the second electrode (46, 46a, 46b) with an adjustable predetermined electric current amplitude in such a manner that with a first level of the adjustable predetermined electric current amplitude a wall contact between (a) the first electrode and/or the second electrode on the one hand and (b) tissue on the other hand is detected and with a second level of the adjustable predetermined electric current amplitude a formation of ice within the biological material being located in between the two stimulated electrodes is recognized, wherein the second level is below 0.01 mA, wherein the second level is smaller than the first level. (a) the first electrode and/or the second electrode on the one hand and (b) tissue on the other hand is detected and