A competitive binding assay is used to determine whether a non-nucleic acid molecule from a library of non-nucleic acid molecules binds to a target. The non-nucleic acid molecule competes with a labeled nucleic acid ligand for binding to the target which may be immobilized. Detecting displacement of labeled nucleic acid ligand from a complex of the labeled nucleic acid ligand and the target determines binding of the non-nucleic acid molecule to the target. The nucleic acid ligand may be immobilized and contacted with a labeled target to form a complex. Adding a non-nucleic acid molecule to the complex displaces labeled target from the complex, and detecting displacement of the labeled target determines binding of the non-nucleic acid molecule to the target. Labeled nucleic acid ligand or labeled target displaced from or remaining in the complex can be detected for detecting displacement. Nucleic acid ligands that bind to the target are identified by the SELEX method. The assay provides a high throughput screening method for determining whether a non-nucleic acid molecule binds to a target.