The diffusion in an ordered alloy under irradiation is modelled on a rigid lattice with two atomic exchange mechanisms acting in parallel: thermally activated and forced jumps. Two descriptions are proposed and applied to the A2-B2 disorder-order transition in bcc compounds: a deterministic kinetic method in the Bragg-Williams approximation and Monte Carlo simulations. Dynamical equilibrium phase diagrams under irradiation are built; microstructural evolutions are studied: a new mechanism for irradiation induced elimination of antiphase boundaries is identified as well as the various dissolution modes of ordered precipitates. The shift from second to first order of the A2-B2 transition, predicted by the model, has been experimentally checked by 1 MeV electron irradiations of a FeAl alloy. 60 figs., 135 refs.