A method for the detection or quantitation of unlabeled target analyte in a biological sample, the method comprising labeling a target analyte for a biological sample suspected of containing unlabeled target analyte with an acridinium compound to form a labeled target analyte and providing the labeled target analyte to the biological sample, or providing the labeled target analyte to the biological sample, wherein the acridinium compound comprises an acridinium nucleus having an electron-donating substituent directly attached to the acridinium nucleus, with the electron-donating substituent attached 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.