The paper for the first time focuses on the fundamental geocryological goal - direct determining of permafrost agewith implications in many fields of geo- and bioscience. In general, the duration of the permafrost existence does notcoincide with the age of the sediments. Therefore, a cross-section of the cryolithosphere (except the syngeneticallyfrozen layers, that were frozen upon deposition and never had thawed) represents a sequence with known age of thesediments and with permafrost age, which is unknown or different to the sediment ages.Theoretically, the problem could be solved using the approach of nuclear physics. We present a method of permafrostdating with the cosmogenic radionuclides 36Cl and 10Be in ice as a natural chronometer. The principal advantage ofthe proposed dating method for permafrost studies is based on the determination of the time of 36Cl and 10Be fixationthat corresponds to the age of the ice. As the first application, ice wedges are dated. As signals, the 36Cl and 10Beratios are used. 36Cl and 10Be are produced in the atmosphere by nuclear and spallation reactions of cosmic rays withargon and nitrogen or oxygen, respectively. Stable chlorine enters the atmosphere from the oceans and is containedin the precipitations. The ratio does not depend on chloride concentrations in precipitations and on sublimation ofsnow. In-situ production of 36Cl in ice via neutron capture reactions on chlorine and of 10Be via cosmic ray inducedreactions on oxygen are calculated.Preliminary analysis of the results supports feasibility of the permafrost dating. 36Cl/Cl ratios in late and middle PleistoceneIcy Complexes samples from the cape Svjatoy Nos on the Laptev Sea coast (72° N, 140° E) were measured byaccelerator mass spectrometry. The time difference between the formations of these Complexes was estimated as 0.4million years. This time difference compares reasonably well with a time difference estimated by traditional geologicalmethods. Dating limit based on the presented method corresponds to an age limit of 3 million years. This intervalcovers all possible Arctic permafrost horizons and the significant (from late Pliocene) part of Antarctic permafrost. Asa next approach step, 36Cl and 10Be in ice-cement and segregated ice will be dated. To develop the cosmogenic datingof permafrost age, it is necessary to correlate these data with the geological and permafrost history.