In this work, the optical and electronic characteristics of MoS2(n,n) and MoSe2(n,n) nanotubes and 1D van der Waals nanoheterostructures based on them are determined from first principles. It is shown that with an increase in the diameters of MoS2(n,n) and MoSe2(n,n) nanotubes, their bandgaps increase (in MoS2(n,n), the gap varies from 0.27 eV to 1.321 eV, and in MoSe2(n,n) from 0.153 eV to 1.216 eV). It was found that with an increase in the diameter of the nanotubes, the static permittivity decreases; van der Waals nanostructures of MoS2(8,8)@MoSe2(16,16) and MoS2(6,6)@MoSe2(14,14) consisting of coaxially compound MoS2(8,8) and MoSe2(16,16), MoS2(6,6) and MoSe2(14,14), respectively, have high static dielectric permittivitiesof 6. 5367 and 3.0756. Such nanoheterostructures offer potential for developing various nanoelectronic devices due to the possibility of effective interaction with an electric field. Studies revealed that the van der Waals nanostructures MoSe2(6,6)@MoS2(14,14) and MoSe2(8,8)@MoS2(16,16) exhibit a semiconductor nature with bandgap widths of 0.174 eV and 0.53 eV, respectively, and MoS2(6,6)@MoSe2(14,14) and MoS2(8,8)@MoSe2(16,16) exhibit metallic properties. Stepped areas of Coulomb origin with a constant period at a voltage of 0.448 V appear on the current–voltage characteristic of the van der Waals nanoheterodevices. It is found that MoSe2(6,6)@MoS2(14,14) and MoSe2(8,8)@MoS2(16,16) nanodevices transmit electric current preferentially in the forward direction due to the formation of a nanoheterojunction between semiconductor nanotubes with different forbidden band values. The fundamental regularities obtained during the study can be useful for the further development of electronic components of nano- and microelectronics.