The　order-disorder　transformation　of　intermetallics　is　of　fundamental　and　technical　importance.　The　ordering　behaviours　of　the　0　phase　based　on　Ti2AlNb　alloys　are　predicted　by　combining　thermodynamic　model　with　ab　initio　calculation.　The　site　occupying　tendencies　of　the　constituent　elements　are　studied　for　the　first　time　theoretically　without　referring　experimental　data　as　input.　The　predicted　results　show　that　Al　atoms　always　tend　to　occupy　the　gamma(4c1)　sublattice,　Ti　atoms　tend　to　occupy　the　alpha　(8g)　sublattice　and　Nb　atoms　the　beta　(4c2)　sublattice.　The　ordering　tendencies　of　Ti　and　Nb　atoms　decrease　with　the　increase　of　temperature,　while　the　site　occupation　of　Al　atoms　is　weakly　dependent　on　the　temperature.　The　order-disorder　transformation　belongs　to　a　second-order　transition　with　a　continuous　character.　It　is　also　predicted　that　for　the　nonstoichiometric　O　phase　with　At　contents　higher　than　25　at.%,　the　site　occupancies　of　the　excess　Al　atoms　prefer　the　P　sublattice.　The　predicted　site　occupancy　fractions　and　order　parameters　agree　well　with　the　reliable　experimental　data.　The　prediction　has　been　improved　compared　with　the　Gorsky-Bragg-Williams　model,　as　well　as　our　early　LMTO-ASA　calculations.　(c)　2007　Elsevier　Ltd.　All　rights　reserved.