Our paper reviews the planned space-based gamma-ray telescope GAMMA-400 and evaluates in details its opportunities in the field of dark matter ( DM ) indirect searches . We estimated the GAMMA-400 mean sensitivity to the diphoton DM annihilation cross section in the Galactic center for DM particle masses in the range of 1–500 GeV . We obtained the sensitivity gain at least by 1.2–1.5 times ( depending on DM particle mass ) with respect to the expected constraints from 12 years of observations by Fermi-LAT for the case of Einasto DM density profile . The joint analysis of the data from both telescopes may yield the gain up to 1.8–2.3 times . Thus the sensitivity reaches the level of annihilation cross section \langle \sigma v \rangle _ { \gamma \gamma } ( m _ { \chi } = 100 ~ { } \mbox { GeV } ) \approx 10 ^ { -28 } cm ^ { 3 } /s . This will allow us to test the hypothesized narrow lines predicted by specific DM models , particularly the recently proposed pseudo-Goldstone boson DM model . We estimated the GAMMA-400 sensitivity to axion-like particle ( ALP ) parameters by a potential observation of the supernova explosion in the Local Group . This is very sensitive probe of ALPs reaching the level of ALP-photon coupling constant g _ { a \gamma } \sim 10 ^ { -13 } ~ { } \mbox { GeV } ^ { -1 } for ALP masses m _ { a } \lesssim 1 neV. We also calculated the sensitivity to ALPs by constraining the modulations in the spectra of the Galactic gamma-ray pulsars due to possible ALP-photon conversion . GAMMA-400 is expected to be more sensitive than the CAST helioscope for ALP masses m _ { a } \approx ( 1 - 10 ) neV reaching g _ { a \gamma } ^ { min } \approx 2 \cdot 10 ^ { -11 } ~ { } \mbox { GeV } ^ { -1 } . Other potentially interesting targets and candidates are briefly considered too .