A delayed coincidence method, time-interval analysis (TIA), has been applied to successive alpha- alpha decay events on the millisecond time-scale. Such decay events are part of the (220)Rn-->(216)Po ( T(1/2) 145 ms) (Th-series) and (219)Rn-->(215)Po ( T(1/2) 1.78 ms) (Ac-series). By using TIA in addition to measurement of (226)Ra (U-series) from alpha-spectrometry by liquid scintillation counting (LSC), two natural decay series could be identified and separated. The TIA detection efficiency was improved by using the pulse-shape discrimination technique (PSD) to reject beta-pulses, by solvent extraction of Ra combined with simple chemical separation, and by purging the scintillation solution with dry N(2) gas. The U- and Th-series together with the Ac-series were determined, respectively, from alpha spectra and TIA carried out immediately after Ra-extraction. Using the (221)Fr-->(217)At ( T(1/2) 32.3 ms) decay process as a tracer, overall yields were estimated from application of TIA to the (225)Ra (Np-decay series) at the time of maximum growth. The present method has proven useful for simultaneous determination of three radioactive decay series in environmental samples.