The Moessbauer technique was used to investigate the hyperfine interaction of /sup 161/Dy and /sup 151/Eu in cubic rare earth tungsten bronzes: Dysub(0.18)WO/sub 3/ and Eusub(0.18)WO/sub 3/. Well resolved hfs spectrum was obtained at 4.2 K for Dysub(0.18)WO/sub 3/. The effective hf field approximation sufficed to interpret the spectrum. The obtained hyperfine interaction parameters were: -g/sub 0/..beta..sub(N)Hsub(eff)=(805+-19) Mc/s and e/sup 2/qQ/sub 0//4 = (506+-56) Mc/s. These results imply that ground doublet of Dy/sup +3/ ion in bronze is a Kramers doublet Vertical Bar+-15/2> with asymmetrical hyperfine tensor Asub(z) non equal to 0, Asub(x) = Asub(y) = 0 and that local crystalline field at RE metal in tungsten bronze at 4.2 K cannot be cubic. From ME absorption spectra of Eusub(0.18)WO/sub 3/ taken at 4.2 K, 78 K and 300 K the values of quadrupole interaction constants for bronze lattice and its temperature dependence were obtained. These data indicate that a phase transition from the high temperature ideal perovskite structure to a distorted one occurs in RE bronzes and that the distortion concerns the nearest tungsten-oxygen environment of RE ion.