In this letter we present photoluminescence measurements with different excitation energies on single-layer MoS$_2$ and MoSe$_2$ in order to examine the resonance behavior of the conservation of circular polarization in these transition metal dichalcogenides. We find that the circular polarization of the emitted light is conserved to 100% in MoS$_2$ and 84% / 79% (A/A$^-$ peaks) in MoSe$_2$ close to resonance. The values for MoSe$_2$ surpass any previously reported value. However, in contrast to previous predictions, the degree of circular polarization decreases clearly at energies less than the two-phonon longitudinal acoustic phonon energy above the resonance. Our findings indicate that at least two competing processes underly the depolarization of the emission in single-layer transition metal dichalcogenides.
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