For the determination of an immunologically detectable substance based on a heterogeneous immunoassay by use of a solid phase on which one of the immunologically active reaction components is bound, a reaction vessel is used as the solid phase on the inner surface of which streptavidin or avidin is bound in such an amount that 0.1 to 2.5 .mu.g are present per ml reaction volume.A suitable reaction vessel for this has optically transparent wall areas which face one another and has avidin or streptavidin coated walls which are at least partially within the inner wall region intended as a receptacle for liquid, wherein the inner space of the container intended as a receptacle for liquid and the respective streptavidin or avidin content of the coating are so matched that 0.1 to 2.5 .mu.g streptavidin or avidin are present per ml reaction volume.