The invention discloses a Non-Equilibrium Capillary Electrophoresis of Equilibrium Mixtures (NECEEM) method and NECEEM-based practical applications. The NECEEM method is a homogeneous technique, which, in contrast to heterogeneous methods, does not require affixing molecules to a solid substrate. The method of the invention facilitates 3 practical applications. In the first application, the method allows the finding of kinetic and thermodynamic parameters of complex formation. It advantageously allows for revealing two parameters, the equilibrium dissociation constant, K.sub.d, and the monomolecular rate constant of complex decay, k.sub.off, in a single experiment. In the second practical application, the method of this invention provides an approach for quantitative affinity analysis of target molecules. It advantageously allows for the use of affinity probes with relatively high values of k.sub.off. In the third practical application, the method of this invention presents a new and powerful approach to select target-binding molecules (ligands) from complex mixtures. Unique capabilities of the method in its third application include but not limited to: (a) the selection of ligands with pre-determined ranges of kinetic and thermodynamic parameters of target-ligand interactions, (b) the selection of ligands present in minute amounts in complex mixtures of biological or synthetic compounds such as combinatorial libraries of oligonucleotides, and (c) the selection of ligands for targets available in very low amounts. In particular, the method of this invention provides a novel approach for the selection of oligonucleotide aptamers. The NECEEM-based method can be used for discovery and characterization of drug candidates and the development of new diagnostic methods.