One of the topical problems of contemporary physics is a possible variability of the fundamental constants. Here we consider possible variability of two dimensionless constants which are most important for calculation of atomic and molecular spectra (in particular, the X-ray ones): the fine-structure constant α=e2/ℏc and the proton-to-electron mass ratio μ=mp/me. Values of the physical constants in the early epochs are estimated directly from observations of quasars-the most powerful sources of radiation, whose spectra were formed when the Universe was several times younger than now. A critical analysis of the available results leads to the conclusion that the present-day data do not reveal any statistically significant evidence for variations of the fundamental constants under study. The most reliable upper limits to possible variation rates at the 95% confidence level, obtained in our work, read: |α̇/α|<1.4×10-14 yr-1, |μ̇/μ|<1.5×10-14 yr- on the average over the last 1010 yr. .