Basing on a quantitative analysis of DTA heat flow measurements the compositions of eutectic and peritectic reactions in complicated systems can be sensitively determined. In addition to the conventionally used DTA onset temperatures, the quantitative analysis of the corresponding heat flows provides important further information which significantly improve the determination of phase relations in complicated systems. The general concept is demonstrated for simple model systems. The sensitivity of detection and the separability of the DTA events will be discussed in detail. The applicability of the method is proved for two complicated examples from the Y-Ba-Cu-O system : (1) the quasibinary section YBa2Cu3O7-delta-BaCuO2 and (2) the ternary eutectics YBa2Cu3O7-delta-BaCuO2-CuO.