This process makes it possible to manufacture articles of any shape by stamping, in which articles the matrix of the alloy has to have a coarse-grained structure. According to the invention, a partial hot-forming operation is carried out by stamping a blank made of an oxide-dispersion-strengthened alloy, especially a nickel-based alloy, having an initial ultrafine-grained structure, in order to form a shaped component, this shaped component is subjected to a secondary recrystallization heat treatment so as to develop an abnormal grain growth, and then a new hot-forming operation is carried out by stamping in order to give the recrystallized shaped component the final shape of the article.