The structural evolution under Am-241 self-irradiation of U1-xAmxO2 +/-delta transmutation fuels (with x <= 0.5) was studied by X-ray diffraction (XRD). Samples first underwent a preliminary heat treatment performed under a reducing atmosphere (Ar/H-2(4%)) aiming to recover the previously accumulated structural defects. Over all measurements (carried out over up to a full year and for integrated doses up to 1.5 X 10(18) a-decay events.g(-1)), only fluorite U1-xAmxO2 +/-delta solid solutions were observed. Within a few days after the end of the heat treatment, each of the five studied samples was slowly oxidized as a consequence of their move to air atmosphere, which is evidenced by XRD by an initial sharp decrease of the unit cell parameter. For the compounds with x <= 0.15, this oxidation occurred without any phase transitions, but for U0.6Am0.4O2 +/-delta and U0.5Am0.5O2 +/-delta, this process is accompanied by a transition from a first fluorite solid solution to a second oxidized one, as the latter is thermodynamically stable in ambient conditions. In the meantime and after the oxidation process, Am-241 alpha self-irradiation caused a structural swelling up to similar to 0.8 vol %, independently of the sample composition. The kinetic constants of swelling were also determined by regression of experimental data and are, as expected, dependent on x and thus on the dose rate. The normalization of these kinetic constants by sample alpha-activity, however, leads to very close swelling rates among the samples. Finally, evolutions of microstrain and crystallite size were also monitored, but for the considered dose rates and cumulated doses, alpha self-irradiation was found, within the limits of the diffractometer used, to have almost no impact on these characteristics. Microstrain was found to be influenced instead by the americium content in the materials (i.e., by the impurities associated with americium starting material and the increase of cationic charge heterogeneity with increasing americium content).