Non-Systematic Evolution of Ligands by EXponential enrichment (SELEX)selection of aptamers, a novel technology for aptamer selection from libraries of random DNA (or RNA) sequences, involves repetitive steps of partitioning without polymerase chain reaction (PCR) amplification between them. This selection is based on non-equilibrium capillary electrophoresis of equilibrium mixtures (NECEEM) and has exceptionally high efficiency. In this paper, a mathematical analysis was carried out to predict the levels of enrichment of non-SELEX selection under different conditions such as different protein concentrations and different efficiencies of partitioning. Investigated results suggest that the magnitude of the bulk affinity (k d) being 104 or 105 μM for the initial pool has no obvious effect on selective enrichment and that the first, second, and third rounds of non-SELEX selection have different optimum protein concentration values [T f] that give maximum enrichment levels when [T f] ranges from 0.0005 to 0.5 μM. The significance of analyzing selective enrichment of NECEEM-based non-SELEX with the efficiency of partitioning target-bound ligands from free ligands has been demonstrated.