The　Gd-Bi　and　the　Ho-Bi　systems　were　thermodynamically　assessed　by　CALPHAD　(CALculaton　of　PHAse　Diagram)　approach　based　on　the　available　experimental　data　including　thermochemical　properties　and　phase　equilibria.　The　formation　enthalpies　(at　0　K)　of　the　compounds　of　the　Gd-Bi　and　the　Ho-Bi　systems　were　calculated　by　the　first-principles　method　and　used　in　the　present　thermodynamic　optimization.　The　excess　Gibbs　energies　were　formulated　with　the　Redlich-Kister　polynomial.　The　intermetallics,　Gd5Bi3,　Gd　4Bi3,　GdBi,　GdBi2,　Ho5Bi3　and　HoBi,　were　treated　as　stoichiometric　compounds.　A　good　agreement　between　the　calculated　results　and　the　experimental　data　was　obtained.　©　2013　Elsevier　Ltd.