An Accelerator Mass Spectrometry system has been developed using the 14UD tandem accelerator at the Australian National University. It has been used for Cl-36 measurements on groundwater samples from the Murray Basin in southeastern Australia. Measurements of C-14 have also been made on the same groundwaters. The information can be combined with stable isotope ratios and other data to illustrate the occurrence of processes such as radioactive decay and local recharge in different aquifers.