In　this　study,　the　structural,　elastic,　and　thermodynamic　properties　of　DO19　and　L12　structured　Co3X　(X　=　W,　Mo　or　both　W　and　Mo)　and　μ　structured　Co7X6　were　investigated　using　the　density　functional　theory　implemented　in　the　pseudo-potential　plane　wave.　The　obtained　lattice　constants　were　observed　to　be　in　good　agreement　with　the　available　experimental　data.　With　respect　to　the　calculated　mechanical　properties　and　Poisson＇s　ratio,　the　DO19-Co3X,　L12-Co3X,　and　μ-Co7X6　compounds　were　noted　to　be　mechanically　stable　and　possessed　an　optimal　ductile　behavior;　however,　L12-Co3X　exhibited　higher　strength　and　brittleness　than　DO19-Co3X.　Moreover,　the　quasi-harmonic　Debye-Grüneisen　approach　was　confirmed　to　be　valid　in　describing　the　temperature-dependent　thermodynamic　properties　of　the　Co3X　and　Co7X6　compounds,　including　heat　capacity,　vibrational　entropy,　and　Gibbs　free　energy.　Based　on　the　calculated　Gibbs　free　energy　of　DO19-Co3X　and　L12-Co7X6,　the　phase　transformation　temperatures　for　DO19-Co3X　to　L12-Co7X6　were　determined　and　obtained　values　were　noted　to　match　well　with　the　experiment　results.