  Precise radial velocity measurements (delta v/c ~ 10^{-7}) of FeII lines in
damped Ly-alpha systems from very high quality VLT/UVES spectra of quasars
HE0515-4414 and Q1101-264 are used to probe cosmological time dependence of the
fine structure constant, alpha. It is found that between two redshifts z1 =
1.15 and z2 = 1.84 the value of Delta alpha/alpha changes at the level of a few
ppm: (alpha_z2 - alpha_z1)/alpha_0 = 5.43 +/- 2.52 ppm. Variations of alpha can
be considered as one of the most reliable method to constrain the dark energy
equation of state and improvements on the accuracy of the wavelength
calibration of QSO spectra are of great importance.
