The most probable and dangerous radionuclides which can appear in waste water of atomic power stations after accidents or terrorist acts are Cs-134.137, Sr-90, I-129. Moreover, the radionuclides Cs-137, 90Sr and Co-60 are also most attractive for terrorists to use in dirty bombs. As a result of the disasters the radionuclides can contaminate drinking water. Generally, tap water is decontaminated at water supply stations. Nevertheless it is very important to have sorbents and household drinking water filters in stocks to prevent panic of populace and consequences of emergency cases at the water supply stations. As the concentration of Na+, K+, Ca2+, Mg2+, CI- ions in potable water can have the value of 100-500 mg/l and the concentration of radionuclides is very low, the sorbents must have high selectivity and distribution coefficient of Cs+, Sr2+, Co2+, I- ions. Unfortunately most of known resins cannot be used for these purposes. The created technology of producing cationic and anionic exchange fibroid sorbents on the base of polyacrylonitrilic fibers is described in the paper. Chemical characteristics of the sorbent and filters were investigated. The static exchange capacity is 3-4 meq/g for cationic sorbents and 1-2 meq/g for anionic sorbents. The removal coefficient of listed radionuclides from drinking water by the filter is 10(2)-10(3). After the Chernobyl accident the Academy of Sciences and KGB of Ukraine tested the household filters with fibroid sorbents and ten thousands filters were produced in the Institute of Nuclear Physics of Uzbekistan and given to Ukraine through "Isotope" Corp. (USSR). The experience of using the filters for purification of drinking water from radionuclides in Chernobyl region is described in the paper. High technical and chemical characteristics of the sorbents have been confirmed by tests in certified labs of Germany, USA, Korea, India and Russia.