Dielectric measurements are reported in the frequency range 10(-3)-10(5) Hz and time range 10(-3)-10(3)s on samples of sand and soil of different purity, i.e. washed and unwashed, and in a range of relative humidities (RH) between 7% and 97%. All samples show, at low frequencies, a tendency to low-frequency dispersion, with varying degrees of complications from other processes and with a strong influence of purity and RH. At high frequencies there is a low-loss response independent of purity and RH arising from the bulk grains, while at intermediate frequencies evidence is seen for the first time of ''dipole-like'' response due to the individual grains acting as ''giant dipoles''. Time-domain measurements show nearly time-independent charging and discharging currents with ''battery-like'' response, proving the dominance of electrochemical processes. A discussion is given of the observed behaviour in terms of the current understanding of dielectric processes in humid systems.