By means of first-principle FLAPW-GGA calculations, we have investigated the electronic properties of the newly discovered layered quaternary systems SrFeAsF and CaFeAsF as parent phases for a new group of oxygen-free FeAs superconductors. The electronic bands, density of states, Fermi surfaces, atomic charges, together with Sommerfeld coefficients γ and molar Pauli paramagnetic susceptibility χ have been evaluated and discussed in comparison with oxyarsenide LaFeAsO -a parent phase for a new class of high-temperature (Т С ~ 26-56К) oxygen-containing FeAs superconductors. Similarity of our data for SrFeAsF and СаFeAsF with the band structure of oxygen-containing FeAs superconducting materials may be considered as theoretical background specifying the possibility of superconductivity in these oxygen-free systems. ______________________________________________ * E-mail address: shein@ihim.uran.ru 1