The formation of stable and metastable AlFe and AlFeSi intermetallic phases were investigated as a function of their emerging conditions. In the binary system the forming regions of the AlFe intermetallic phases were given as the function of the Fe content and the cooling rate. The transformation of non-equilibrium phases occurs to give the Al6Fe compound < 400 degrees C, while > 400 degrees C the Al3Fe intermetallic phase appears. In the ternary system it is established that formation of the equilibrium phase belonging to a certain phase field is replaced by the non-equilibrium phase forming of the equilibrium phases existing in the "higher" phase region. The thermostability of cubic alpha-AlFeSi is lower the further its emerging condition from the equilibrium states.