The formation of homogeneous highly supersaturated (up to 23 at.% Be and 31.4 at.% Be in a Co–Be alloy and a Cu–Be alloy, respectively) solid solutions having the same composition as the initial liquid ($C_0$) is revealed in the Co–Be and Cu–Be alloys by the method of quenching from the liquid state (QLS). At the maximum cooling rates (10$^7$ K/s) sufficient to form an amorphous solid state, it is not possible to prevent ordering processes in the congruent equiatomic phase of CsCl-type Co–Be. At the same time, for a Cu–Be alloy, it is shown that, under the QLS conditions, a hybrid interstitial–substitutional-type solid solution can be formed. As experimentally confirmed, under the QLS conditions, a significant supercooling of the melt below the decomposition temperature of the phases of the eutectoid composition, namely, $\beta_1$ and $\beta$ in the Co–Be and Cu–Be alloys, respectively, is took place. The positive role of the QLS method in increasing of the level of the mechanical and hard-magnetic characteristics in rapid-quenched films is shown.