Studies of the LaOAgS-type compounds among alkaline earth – Al (Ga) fluoride tetrelides revealed the existence of two new compounds BaFAlSi and BaFAlGe which are the first representatives of fluoride tetrelides; they also are the first representatives of the structure type not involving transition metals. No compound of the structure type is formed for strontium and gallium. Quantum chemical calculations indicate that only these two compounds are thermodynamically stable; the structure is probably stabilized by ionic interactions in the FeSe-like anionic slabs, which are relatively weak for bonds formed between triels and tetrels that are close in electronegativity.