There is a growing interest in collection of data concerning human exposures to naturally occurring alpha-emitting radionuclides (e.g. in mines, dwellings, building materials, industrial wastes, coal fuel cycle, water supply, soil, plants, etc). Most of such studies is incomplete for the following reasons: 1) In radon measurements the contribution of thoron is generally neglected. 2) The determination of equilibrium factor is complicated or not possible at all. 3) Short- and long-term concentration fluctuations cause difficulties in obtaining representative mean values. 4) The plate-out effect is generally not taken into account. We have studied a variety of simple methods that could be used to overcome some of these difficulties by using cups equipped with two or more alpha-sensitive nuclear track detectors. A theoretical foundation of the quantitative measurements with such devices is presented. Experimental data are reported on radon, radon daughters and thoron concentrations measured by multi-detector devices in cave soil gas and in air of Hungarian dwellings.