The phase equilibria of the ternary Al-AlCo-AlNi system were investigated around the decagonal phase. Isopleths with 70, 71.5 and 72.5 at.% Al and with 10 and 13 at.% Ni are elaborated with the aid of differential thermoanalysis, magnetothermal analysis, optical microscopy and transmission electron microscopy. These are based on results of samples of more than 80 different compositions and on data from other isopleths.