Selected A-site cation-ordered BaLnMn(2)O(6) were investigated by neutron diffraction technique in terms of the structural modification ongoing with the oxygen release during annealing in reducing conditions. Kinetics of the structural transformations between oxidized BaLnMn(2)O(6) (O-6), partially reduced BaLnMn(2)O(5.5) (O-5.5) and fully reduced BaLnMn(2)O(5) (O-5) were measured in 200-500 degrees C range in 5 vol% H-2 in Ar. Studies revealed that both O-6-O-5.5 and O-5.5-O-5 transitions for all samples occur according to a two-phase mechanism, but the phases undergo slight modification of their structural parameters. The Y-containing material showed decreased tendency of formation of oxygen vacancy-ordered BaYMn2O5.5. Moreover, kinetics of the transitions for Pr- and Nd-containing oxides was found to be more constrained by surface reaction and nucleation processes at the initial stage, while the following oxygen release from O-5.5 phase was found to be limited rather by the oxygen diffusion, which is in opposite to BaYMn2O5+delta. The obtained results indicate that ionic radius of Ln(3+) has a direct influence on the mechanism of the oxygen release process from BaLnMn(2)O(6), influencing the oxygen storage-related performance.