In addition to property anomalies, a distinguishing feature of the intermediate phase is the qualitative change of the crystallization or recrystallization interval (Q∆LS) that occurs at congruent and incongruent melting phases, at eutectic or eutectoid points, at the ends of eutectic or eutectoid horizontals, and also at any nonmonotonicity of the liquidus, since the solidus or solidoid is a horizontal in eutectic or eutectoid systems. A technique has been developed that allows us to associate anomalies in the properties of industrial alloys with state diagrams based on the first established criterion - a qualitative change (length in temperature) of the crystallization (recrystallization) interval (Q∆LS), as well as with a difference in the structural heredity (genealogy) of the component atoms that make up dual system. A joint analysis of the anomalies in the properties of binary alloys with state diagrams (based on the established criterion (Q∆LS)) allows us to relate the latter to the presence of intermediate phases in Al − Si, Fe − C, Al − Cu systems. The intermediate phases AnBm-Q∆LS explaining the anomalies of properties are declared: ~Al7Si, Al41Cu9 − correspond to the eutectic point; Fe24C − eutectoid point; Al11Si, AlSi6 − the bend of the liquidus; Fe42C − bending liquidoid; Al49Cu, Al98.5Si1.5 − the end of the eutectic horizontal; Cu4Al, Cu7Al3 − to the ends of the eutectoid horizontal.