A method is revealed for the quantitative determination of the proportion of the free form of a thyroid hormone ligand in a sample of a biological fluid in which the ligand is present partly in the free form and also partly in a form in which it is bound to physiological binding proteins. In the first step, a ligand derivative of the thyroid hormone with an immunoglobulin, a labelled specific binder, and a test tube whose walls are coated with an excess of a protein material are provided. In the second step, a sample of the biological fluid containing an unknown amount of the free thyroid hormone ligand, a solution containing a known amount of the ligand derivative, and a solution containing a known, less than stoichiometric amount of the labelled specific binder are added to the test tube to form a liquid reaction mixture. In the third step, the reaction mixture is incubated to allow the free thyroid hormone ligand and the ligand derivative in the liquid reaction mixture to compete for the binding sites of the labelled specific binder, and to allow, in a concomitant slower reaction, the binding of the immunoglobulin part of the ligand derivative to the excess of the protein material on the walls of the test tube. In the fourth step, the remaining liquid reaction mixture is removed from the test tube. In the final steps, the amount of labelled specific binder bound to the walls of the test tube is determined and the amount of the free thyroid hormone ligand calculated.