By establishing suitable high-temperature preparation conditions We were able to grow the first RuO42--doped crystals of K2CrO4, K2SeO4, Cs2MoO4, BaSO4, BaCrO4, and BaSeO4. Their polarized absorption spectra at low temperatures are reported and discussed. These are very different from the ruthenate(tl) spectra in the literature, and the lack of resemblance between calculated and measured spectra of ruthenate(VI)-assumed to be RuO42- in the past-is easily understood. The (3)A(2) --> (1)A(1) spin-flip transition of RuO42- peaks at approximate to 7100 cm(-1). Stronger bands due to (3)A(2) --> T-3(2) and T-3(1) are observed in the vis around 13 500 and 16 500 cm(-1), respectively, giving rise to the green-blue color of most samples. In the BaSO4 host the (1)A(1) absorption line is split into three differently polarized components exhibiting a strong temperature dependence. This can be analyzed in terms of a Boltzmann population with three levels at 0, 13, and 18 cm(-1), corresponding to the three spinor components of the (3)A(2) ground state. In order to better understand the major changes Which occur on going from the 3d(2) to the 4d(2) electron configuration the spectroscopic data of RuO42- are compared with those of CrO44-, MnO43-, and FeO42-.