  We have determined the apsidal motion rate of 27 double-lined eclipsing
binaries with precise
  physical parameters. The obtained values, corrected for their relativistic
contribution, yield precise empirical parameters of the internal stellar
density concentration. The comparison of these results with the predictions
based on new theoretical models shows very good agreement.
  Small deviations are identified but remain within the observational
uncertainties and the path for a refined comparison is indicated.
