Human genes HBB, HBD and F9 belong to the hematopoiesis system. The deficiency or excess of these genes' products is the cause of hereditary thalassemias of various severity and haemophilia B Leyden. Previously, it was shown that a number of annotated single-nucleotide polymorphisms of TATA boxes of these genes associated with the occurrence of β-and δ-Thalassemia affect the interaction with the TATA-binding protein, the interaction changing proportionally with the change in the number of gene products. In the present work, we investigate the effect of rare not annotated single-nucleotide polymorphisms (SNPs) of TATA boxes of these genes with an unknown manifestation on the TATA-binding protein interaction. To study the kinetic cha-racteristics of TBP/TATA complex formation in vitro, doublestranded oligodeoxynucleotides identical to the TATA-containing portions of the promoters of the HBB, HBD and F9 genes ("normal" and minor alleles) and recombinant human TBP were used. It was shown that the TATA-box SNP of -25A> C (rs281864525) and the deletion of the -25AA (rs63750953) TATA-box of the β-globin gene have the same effect on the TBP/TATA affinity, which decreases 3-folds in both cases. However, the effect of these substitutions on the rate of the TBP/TATA complex formation is significantly different: SNP -25A> C decreases the rate 5-fold, and the deletion decreases the rate more than 7-fold. The influence of substitutions on the strength of the TBP/TATA complexes has a different effect. If in the case of SNP -25A> C the strength of the complexes increases 1.8-fold, then in the case of the -25AA deletion, the strength of the complexes increases 2.4-fold, even though the affinity of the TATA-binding protein to the TATA box decreases. A comparison of experimental values of affinity (KD) of the TBP/TATA complexes of "normal" and minor alleles with the predicted has shown that data correlate well with each other. The coefficient of linear correlation r = 0.94 (α < 0.0001). A comprehensive approach to the study of rare polymorphisms may lead to the identification of the most sensitive markers of orphan diseases, which will contribute to the development of reliable and rapid methods for their diagnosis and treatment.