A weld process cuitable for repairing precipitation-strengthened superalloys, and particularly gamma prime-strengthened nickel-based superalloys. The process entails forming a weldment in a cavity present in a surface of an article formed of a precipitation-strengthened superalloy. The cavity has a root region and a cap region between the root region and the surface of the article. A solid body formed of a superalloy composition is placed in the root region of the cavity so as to occupy a first portion but not a second portion of the root region. A first filler material formed of a solid solution-strengthened superalloy is then weld-deposited in the second portion of the root region. Subsequently, a second filler material formed of a precipitation-strengthened superalloy is weld-deposited in the cap region of the cavity.