This article  develops  two  bayesian  techniques  to  identify  the  orders of  vector  mixed autogressive  moving  average  processes  namely  the  indirect  and  direct techniques.  The proposed  indirect technique  approximates  the  joint  posterior probability  density  function of  the  coefficients  of the  largest  possible  model  by  a matrix  t  distribution. Then by  employing  a  series  of  tests  of  significance  the  insignificant  coefficients  are  eliminated  and the  model  orders  are  determined.  On the other hand  the proposed  direct  technique derives an approximate  joint  posterior  probability. A wide simulation  study  is conducted to examine  the effectiveness  of the proposed procedures and  compare  their  performance with the well-know  ALC  technique. The numerical  results show  that  the  proposed  techniques  can efficiently  identify the orders  of  vector  autoregressive  moving  average  processes  for  moderate and large  time  series lengths. Moreover  the  indirect  technique dominates the direct and ALC  ones