Phase formation was studied in ion-irradiated multilayer and coevaporated Ni-20 at. % Al films supported by Cu, Mo, and Ni transmission electron microscopy (TEM) grids. Irradiation with either 700-keV Xe or 1.7-MeV Xe, to doses sufficient to homogenize the multilayers (greater-than-or-equal-to 7.5 x 10(15) cm-2), resulted in the formation of metastable supersaturated gamma and HCP phases in both film types. Post-irradiation annealing of multilayers at 450-degrees-C for 1 h transformed the metastable phases to a two-phase gamma + gamma' microstructure. In the absence of Cu, the formation of gamma' appeared to proceed by a traditional diffusional growth mechanism, resulting in small (< 50 angstrom) gamma precipitates in gamma matrix grains. The presence of Cu caused the formation of a dual-phase gamma + gamma' structure (i.e., distinct, equal-sized grains of gamma and gamma') during post-irradiation annealing. It is suggested that copper affected the nucleation of gamma' precipitates and increased the kinetics of growth resulting in the dual-phase morphology. Strong irradiation-induced textures were observed in the multilayers that were less pronounced in the coevaporated films. The texture in the multilayers was attributed to the presence of a slight as-evaporated texture combined with the enhanced atomic mobility due to the heat-of-mixing released during irradiation. The irradiation-induced texture appeared to be necessary for the formation of the dual-phase structure since it likely provided high-diffusivity paths for Cu to diffuse into the film from the TEM grid.