The devitrification behaviour of the rapidly solidified quaternary hafnium-based alloys of Hf65NM17.5TM10Al7.5 composition (NM- noble metal, TM- 3d transition metal) was studied using differential scanning calorimetry. The purpose of the study was to evaluate the influence of composition on the devitrification products at the primary stage. The structure was analysed by using X-ray diffraction and transmission electron microscopy. The formation of the nanoparticles of the Hf-based quasicrystalline icosahedral or cubic cF96 Fd-3m Ti2Ni-type phase about 10 nm in size was observed at the primary devitrification stage in different metallic glasses with close compositions. The icosahedral phase consists of 137-atom Bergmann rhombic triacontahedra. The alloys in systems in which the stable Hf-based cF96 phase exists do not show the formation of the icosahedral phase from the amorphous matrix. The cF96 phase and the icosahedral phase formed by primary devitrification from the amorphous phase may inherit the local order of the icosahedral clusters in the amorphous matrix.