  The two-dimensional rare-earth tri-tellurides undergo a unidirectional
charge-density-wave (CDW) transition at high temperature and, for the heaviest
members of the series, a bidirectional one at low temperature. Raman scattering
experiments as a function of temperature on DyTe$_3$ and on LaTe$_3$ at 6 GPa
provide a clear-cut evidence for the emergence of the respective collective CDW
amplitude excitations. In the unidirectional CDW phase, we surprisingly
discover that the amplitude mode develops as a succession of two mean-field,
BCS-like transitions in different temperature ranges.
