We present direct evidence of the two-step absorption process in anti-Stokes photoluminescence in both ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ and ${\mathrm{InGaP}}_{2}/{\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ heterostructures using two-color picosecond and continuous-wave photoluminescence experiments. We show information about the lifetime of the defect states that participate in the two-step absorption process. As a result, we conclude that the long-lived states rather than excitons play the dominant role in the two-step absorption process. We also study the possible contribution of the two-step absorption process to Stokes carrier transfer in ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ asymmetric double quantum well structures.
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