Two on-line multidimensional HPLC systems are described; one coupling two liquid chromatographic columns (LC/LC), and one coupling liquid and gas chromatography (LC/GC). Theoretical equations relating the reproducibility, accuracy and transfer efficiency to system operating variables such as flow rate, retention time, column efficiency and transfer volume have been developed. These effects are explained and verified using experimental systems. Three major applications are shown for each of the systems. For the LC/LC systems, these include; the analysis of caffeine and theophylline in biological fluids; the analysis of hydrocarbon group types in fuels and oils and the analysis of catecholamines in urine with electrochemical detection. For the LC/GC system, the applications include; the analysis of pesticides in butter, the analysis of hydrocarbon group types in fuels and the analysis of polycyclic aromatic hydrocarbons in petroleum related samples. / Ph. D.