High-frequency electrodeless light sources (HF EDLS) are widely used as bright radiators of narrow and intensive atomic and ionic spectral lines, covering the spectrum from VUV to IR. Main characteristics of HF EDLS are high emitted spectral line intensity, long service life, and in general, narrow spectral line shapes because of low-pressure of filling elements. In this work we give a short overview of the use of HF EDLS, containing Hg, Te, Se, Zn, Pb, As, Sb, Bi, Tl, In, Cd, Sn, in Zeeman Atomic absorption devices for assaying natural, drinking, waste and technical water as well as air, soil, food products and biological samples. The first steps are made for optimization of Ge, Ga, P, S, Ag, Cu HF EDLS. Enhanced detection limits are obtained in comparison with hollow cathode lamps.