  L$\beta\_2$ X-ray satellite spectra of tungsten and gold are calculated using
the Multi-Configuration Dirac-Fock energies and compared with recent
experimental data. New calculations of L$\_1$-L$\_3$M$\_5$ Coster-Kronig
transition energies for tungsten are presented, confirming the origin of the
L$\beta\_2$ visible satellites reported by two experimental groups. We found
the value 5.09 eV for the average energy of the L$\_1$-L$\_3$M$\_5$
Coster-Kronig transition in tungsten. A detailed calculation of the L$\beta\_2$
and L$\beta\_{15}$ satellite spectra was performed for gold.
