Periodic ab initio QM calculations are employed in order to study the structure and redox properties of Cr, Mn, Fe. and Co trivalent transition metal dopants in AlPO-34. Our results show that the local environment of Mn and Co dopants is a distorted tetrahedron due to Jahn-Teller distortions. The bonding between the Me-III dopants and the neighboring oxygens is ionic in nature, and explains the Lewis acidity of the Me-III ions. The replacement energy DeltaE(III) of the 3+ dopant ions in AlPO-34 increases linearly as a function of the Me-O bond distance. Finally, the calculated redox energies of the Me-II/Me-III couples indicate that, among the transition metal ions investigated, Fe is the most stable in the 3+ oxidation state, whereas Mn is the most stable as 2+ ion. Cr and Co, instead, have intermediate behavior and can switch more easily between the two oxidation states. These results contribute to elucidate the mechanistic details of catalytic processes occurring in MeAlPOs.