This paper presents a unifying method for the synthesis of flowsheets for multicomponent separations with sloppy product streams, in which some components being separated may simultaneously appear in two or more product streams. Our goal is to synthesize good separation sequences by using all-sharp, all-sloppy, and both sharp and sloppy separators. After introducing some basic tools and concepts for problem representation, feasibility analysis, and separation synthesis, we propose a unifying classification of all multicomponent separation-sequencing problems into four classes and suggest proper approaches to solving each class of synthesis problems. While we can apply our method with different synthesis tools such as optimization, we use six rank-ordered heuristics in a number of industrial separation problems. The resulting sequences represent good candidates for detailed flowsheet optimization. Our method can be easily applied by hand calculations by practicing engineers, and it has been implemented as an expert system using PROLOG. © 1990, American Chemical Society. All rights reserved.