A detailed thermomagnetic analysis was carried out on a number of alloys along a tie-line in the two-phase (β+β′) region of the Fe-Ni-Al ternary system. The supersaturated solid solution, obtained by quenching an alloy close to the composition Fe2NiAl, broke up very fast at relatively high temperatures （～850℃), precipitation being completed in a little more than a minute. The β′ phase formed at 850℃ still contained about 35 at. % iron, with a Curie point near 400℃. When this alloy, after going through such a short tempering at 850℃ followed by quenching, was heated up to 600-700℃ again, the β′ phase formed during the first tempering continued to decompose rapidly, losing enough iron to become nonmagnetic in not much more than ten minutes. This caused the room-temperature coercive force of the alloy to rise to about 500 Oe. Such a phenomenon is in agreement with Б．Г．Лившнц's. suggestion of "post-precipitation". The magnetic measurements showed, moreover, that the post-precipitatioa of the β′ phase was "reversible", that is, when the alloy was brought up to 850℃ again after quenching from the second tempering at 600-700℃, the β′ phase could recover its equilibrium composition for 850℃ in a few minutes. Decomposition of the supersaturated solid solution Fe2NiAl at relatively low temperatures (below 700℃) was quite slow, and, furthermore, there was considerable evidence that the process was "non-uniform". On the basis of the above findings, the fact that high coercive force in the alloy Fe2NiAl cannot be obtained by quenching from above the solution temperature plus tempering at relatively low temperatures (600-700℃) is interpreted in the light of the single-domain particle theory.