[en] The methods of differential thermal and roentgenophase analyses are used to investigate the points of complete conversion of tertiary mutual systems K, Ba long F, MO₄ (where M-Mo, W) and K, Ba paralel MoO₄, WO₄, as well as lines of complete conversion of quaternary mutual system of K, Ba long F, MoO₄, WO₄. Crystallizable phases in conversion points of tertiary mutual systems are established; exchange reactions and complex formation in tertiary mutual systems of K, Ba long F, MO₄ are found. The stability of binary solid solutions in the K, Ba long MoO₄, WO₄ mutual system is shown; the quaternary mutual K, Ba long F, MoO₄, WO₄ system is presented with six crystallization volumes: BaF₂, KF, a, b, n, e; solid solutions of single-type molybdate and tungstate compounds are stable inside the quaternary mutual system; quaternary invariant points in the system are absent