A process for welding superalloys, and particularly articles formed of gamma prime-strengthened nickel-base superalloys whose chemistries and/or microstructures differ. The process entails forming the faying surface of at least one of the articles to have a cladding layer of a filler material. The filler material may have a composition that is different from both of the articles, or the same as one of the articles. The cladding layer is machined to promote mating of the faying surfaces, after which the faying surfaces are mated and the articles welded together. After cooling, the welded assembly is free of thermally-induced cracks.