Isothermal sections of the Co-Al-Nb system at 800, 1000, 1150, 1200, and 1250 degrees C were experimentally determined by combining results of light-optical as well as scanning electron microscopy, electron-probe microanalysis, and X-ray diffraction measurements with Rietveld analysis of heat-treated alloys and adding some results obtained from solid/liquid diffusion couples. Three polytypes of Laves phases, which are the cubic C15 and the hexagonal C14 and C36 variants, occur as stable phases in the central part of the system The phase equilibria involving these phases were in the focus of the present study. The composition-dependence of the crystallographic properties of the Laves phases as well as the crystal structure parameters of all other occurring intermetallic phases was investigated. As in case of the binary Co-Nb system, the hexagonal Lives phases C14 and C36 are only stable at off-stoichiometric Nb contents The preferential site occupations of the Co-, Al-, and Nb-atoms in the hexagonal lattices of the C14 and C36 Lives phase polytypes were determined by Rietveld analyses For all binary phases except the Nb-rich phase Nb3Al, the solubility for the third element was investigated and the extensions of all phase fields were established. Besides the three Lives phases, the most striking features of the Co-Al-Nb phase diagram are the occurrence of the slowly forming L2(1)-type Heusler phase Co(2)AINb and the extended phase field of the mu phase. The existence of a mu' phase, which was reported in the literature, is not confirmed (C) 2010 Elsevier Ltd All rights reserved.