Water with even a small amount of dissolved solidshas an electrical conductivity orders of magnitude higher than dry rock andis therefore a near-ideal exploration target on Mars for low-frequency, diffusiveelectromagnetic methods. Models of the temperature- and frequency-dependentelectrical properties of rock-ice-water mixtures are used to predict the electromagneticresponse of the Martian subsurface. Detection of ice is difficult unless itis massively segregated. In contrast, liquid water profoundly affects soundings,and even a small amount of adsorbed water in the cryosphere can be detected.Subcryospheric water is readily distinguishable at frequencies as low as 100Hz for fresh water to 10 mHz for brines. These responses can be measured usingeither natural or artificial sources. ULF signals from solar wind and diurnal-heatingperturbations of the ionosphere are likely, and disturbances of regional crustalmagnetic fields may also be observable. Spherics, or ELF-VLF signals fromlightning discharge, would provide optimal soundings; however, lightning maybe the least likely of the possible natural sources. Among the active techniques,only the time-domain electromagnetic (TDEM) method can accommodate a closelyspaced transmitter and receiver and sound to depths of hundreds of metersor more. A ground- or aircraft-based TDEM system of several kilograms candetect water to a depth of several hundred meters, and a system of tens ofkilograms featuring a large, fixed, rover- or ballistically deployed loopcan detect water to several kilometers depth.