Abstract.The results and possibilities of the samples surfaces research by the Doppler method of positron annihilation spectroscopy (PAS) for a monochromatic beam of positrons at the LEPTA facility are presented in this paper. Method with high-resolution sensitivity to defects like vacancies and dislocations allows scanning of the surface and near-surface sample layers to a depth of several micrometers by the method of Doppler broadening of annihilation lines. The opportunities for the development of a PAS method based on the measurement of the positron lifetime in the sample irradiated by ordered flow of positrons from the injector of accelerator complex LEPTA at JINR are discussed.LEPTA facility [1] is a complex consisting of the cryogenic positron source based on the emitter -a radioactive 22Na with an activity of 30 mCi, the electromagnetic PenningMalmberg-Surko trap (PMS) and storage ring. After slowing down in a frozen solid neon layer a monochromatic flux of positrons with intensity up to 10 6 part./sec is formed. The width of the positron spectrum is about 2 eV. This flux can be used for fundamental and applied research [2]. It is possible to carry out layer-by-layer scanning of the defects in subsurface layers of the samples at depths from zero to several micrometers by varying the positron energy in the range of 0.05÷35 Kev. For this purpose, one of three versions of the PAS can be used [3]: observation of correlations in the angular distribution of annihilating photons -gamma quanta (ADAP), measurement of the lifetime of positrons in matter with registration the time distribution of the annihilation photons (TDAP) and the change in energy of the annihilation gamma-quanta -registration of Doppler broadening of annihilation lines (DBAL).The most perspective methods that allow to distinguish the defects of vacancy and dislocation types in samples with a sensitivity of 1 defect per 10 7 atoms in the crystal lattice and at depth resolution of the sample in tenths of nanometer, are the last two versions -TDAP and DBAL. Currently, at the LEPTA complex DBAL PAS method is used with the * Corresponding author: m.eseev@narfu.ru