Assay methods are disclosed involving specific binding reactions which are simplified compared to known methods. A compound capable of producing chemiluminescence is immobilized on a solid support as is a member of a specific binding pair for capturing an analyte from a sample. An activator compound that activates the chemiluminescent compound and is conjugated to a specific binding pair member is added in excess along with the sample to the solid support. Addition of a trigger solution causes a chemiluminescent reaction at the sites where the activator conjugate has been specifically bound. The assay methods are termed non-separation assays because they do not require removal or separation of excess detection label (activator conjugate) prior to the detection step. The methods are applicable to various types of assays including immunoassays, receptor-ligand assays and nucleic acid hybridization assays.