Dielectric behaviour of fatty tissue was investigated from T = 300 K to 4 K and f = 20 Hz to 1 MHz. Characteristic curves were obtained only at low frequencies. With decreasing temperature four important features were detected: the water-ice transition at T = 265 K, a relaxation process of the fat molecules (near 260 K) and one connected with the ice-part (210 K-170 K). The reason for the fourth relaxation at T = 140 K has not been fully understood yet: it may be caused by segmental rotation of the fatty acid molecules or the presence of multiple bonds. The epsilon"-maximum caused by the ice relaxation at T congruent-to 200 K can be used to detect successful application of cryotherapy, i.e. the temperature fall below the minimum value of 233 K.