A method for the detection or quantitation of an analyte in a biological sample is disclosed. The method comprises the steps of selecting a biological sample suspected of containing a target analyte and binding the target analyte in the sample to a binding partner conjugated to an acridinium compound, wherein the acridinium compound comprises an acridinium nucleus having an electron-donating substituent directly attached to the acridinium nucleus at the C.sub.2 position. Chemiluminescent acridinium compounds useful in the method have emission maxima close to or in the near infrared (NIR) region (>590 nm). These chemiluminescent acridinium compounds when used in conjunction with short wavelength-emitting acridinium esters (with emission maxima below 450 nm) can be highly useful labels for the simultaneous detection of multiple target analytes in a single assay.