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The results for the total multi-photon decay rates of the 3p and 4s levels ofhydrogen, presented by D. Solovyev and L. Labzowsky within the cascadeapproximation, are revisited. The corrected results for certain decay channelsdiffer from original ones of those authors sometimes by order of magnitude.Some aspects with respect to the cosmological recombination process areclarified.

Comment on "Two-photon approximation in the theory of electron  recombination in hydrogen" (D. Solovyev and L. Labzowsky, Phys. Rev. A 81,  062509 (2010))