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In superconducting cuprates HBCCO, BSCCO and TBCCO phases Hg-1201, Bi-2201 and Tl-2201 contain a single CuO2 - plane, phases Hg-1212, Bi-2212 and Tl-2212 contain two CuO2 - planes and phases Hg-1223, Bi-2223 and Tl-2223 - three Cu-O2 planes. In HBCCO, BSCCO and TBCCO superconducting CuO2 - blocks are separated by insulating structural blocks (spacers) BaO-HgO-BaO, SrO-BiO- BiO- SrO and BaO-TlO- TlO- BaO respectively. The problem of obtaining optimally doped cuprate samples with n ≥ 3 by a standard method becomes complicated. For example, NMR – spectroscopy studies showed that a copper nuclear magnetic resonance in HgBa2Can-1Cun02n +2 + δ with n ≥ 3 transforms into a doublet which was explained by different levels of oxygen doping in internal (IP) and outer ( OP) CuO2 – planes [3]. The results obtained in the present investigation are as follows: 1. the Andreev and tunneling spectroscopy studies showed that superconductivity in the optimally doped samples of Bi-2201 (Tc = 25 ± 3 K), Hg-1201 (Tc = 93 ± 2 K), Bi-2212 (Tc = 92 ± 2 K), Tl-2212 (Tc = 105 ± 2 K) and Hg-1212 (Tc = 120 ± 5 K) has a single-gap character (Fig. 1 - Fig. 4); 2. superconductivity in Bi-2223 (Tc = 110 ± 5 K), Tl-2223 (Tc = 118 ± 5 K) and Hg-1223 (Tc = 124 ± 5 K) has a multigap character due to the difference in doping levels of internal (IP) and outer (OP) CuO2 - planes in superconducting blocks (Fig. 5 - Fig. 6). All studied junctions in Hg-1201, Hg-1212, Hg-1223, Bi-2201, Bi-2212, Bi-2223, Tl-2212 and Tl-2223 should be considered to be the ballistic type nanocontacts of Sharvin type. The CVC's of the most clean contacts of this kind contain up to (5 - 7) Andreev singularities. For single-gap superconductors the gap magnitude can be determined with sufficient accuracy from linear dependences Vn(1/n). The results of the present investigation for single-layer (n = 1) and two-layer (n = 2) cuprates are in good agreement with data of other authors. Due to the layered structure of cuprates the transport current through nanosteps on the surface of cryogenic cleaves is directed mainly along c-axis. For both tunneling and Andreev regimes the maximal value of the gap Δmax was measured. For phases with n ≥ 3 we have two (or three) subharmonic gap structures and, consequently, two (or three) dependences Vn(1/n). The explanation of this phenomenon can be found in publications, where authors had taken into account the specificity of doping of multilayered HTSC. According to the model proposed in [3], the doping level of internal CuO2-planes in the superconducting block is always lower than the doping level of the outer CuO2-planes. This is caused by the strong screening of the internal CuO2-planes by the outer planes, which are metallized by doping (due to insulator-metal transition). It is for this reason that the NMR resonance at the copper nuclei is transformed into a doublet. A significant difference in doping levels of outer and internal CuO2-planes in the superconducting blocks originated a scenario of coexistence of antiferromagnetism and superconductivity in high-Tc superconductors.