The crystallization process of Fe80P20-xSix amorphous alloys has been studied by electrical resistivity, X-ray diffraction, neutron diffraction, and transmission electron microscopy. This process is classified into two different patterns with a boundary of 6 at%Si. In the alloys containing less than 6 at%Si, alpha-Fe and Fe3P, both of which are stable phases, precipitate from the amorphous matrix directly. In the crystallization of the amorphous alloys containing over 6 at%Si, two complex phases are observed in the early stages. We found that these two phases are isostructural with the alpha-Mn type and beta-Mn type phase. After these two metastable phases disappear, another metastable phase which is probably Fe2P appears. In the final stage of the crystallization, however, existing crystalline phases are stable alpha-Fe (or ordered Fe3Si) and Fe3P. In the isothermal crystallization process of the Fe80P14Si6 amorphous alloy, only the alpha-Mn type phase is observed as the metastable phase at high temperatures such as 683, 703 and 723 K; however, at a lower temperature such as 668 K, no metastable phase is observed. The precipitation of the metastable alpha-Mn type and/or beta-Mn type phases, which consist of the Frank-Kasper coordination polyhedra, can be closely related to the local structure in these amorphous alloys.