The principles of a dating method based on the cosmic-ray-produced radioisotope /sup 39/Ar are given. Technical requirements such as background and standard gas samples and gas proportional counting systems are described. With samples extracted from Greenland ice it can be demonstrated that /sup 39/Ar ages agree with ages obtained by other methods. First results on ocean water samples show that with this isotope valuable information on ocean mixing and circulation can be expected. /sup 39/Ar results on groundwater samples disagree for some aquifers with conventional /sup 14/C ages; possible explanations are discussed, especially underground production of /sup 39/Ar.