A succinct survey of the state of the art in the analyses of polymer and copolymer systems with respect to difficulties arising from closely related homologs which produce very similar spectra. Discussion of the additional procedures necessary to overcome these problems is given. Specific topics include: trimethylsilylation, chemical cleavage, fusion reactions, oxidative degradation, carboxylic esters, alkyd resins, linear polyesters, polyacrylic esters, polyvinyl esters, polyamides and polyimides, and pyrolysis. The discussion of each topic is supported by one or more references. -- AATA