A method is developed for determining ligand-cell association parameters from a model-free analysis of data obtained with a flow cytometer. The method requires measurement of the average fluorescence per cell as a function of ligand and cell concentration. The analysis is applied to data obtained for the binding of fluoresceinated epidermal growth factor to a human epidermoid carcinoma cell line, A431. The results indicate that the growth factor binds to two classes of sites on A431 cells: 4 X 10(4) sites with a dissociation constant (KD) of less than or equal to 20 pM, and 1.5 X 10(6) sites with a KD of 3.7 nM. A derived plot of the average fluorescence per cell versus the average number of bound ligands per cell is used to construct binding isotherms for four sub-populations of A431 cells fractionated on the basis of low-angle light scatter. The four sub-populations bind the ligand with equal affinity but differ substantially in terms of the number of binding sites per cell. We also use this new analysis to critically evaluate the use of 'Fluorotrol' as a calibration standard in flow cytometry.