This paper considers nonstationary monochromatic radiative transfer in an infinite onedimensional homogeneous medium. The medium is considered to be illuminated by a momentary isotropic point energy source. The optical properties of the medium are characterized by the absorption coefficient α, the single-scattering albedo λ, the mean time t 1 of photon stay in the absorbed state, and the mean time t 2 of its stay on the path between two consecutive scatterings. The exact solution of the nonstationary radiative transfer equation has been obtained for the case t 1 = t 2. Asymptotic expressions have been derived for the source function, for the average intensity, and for radiation flux when points of the medium are located at large optical distances from the power source |τ| ≫ 1 and for small absorption of light in the medium (1 − λ ≪ 1), assuming that t 1 ≫ t 2, t 1 ≪ t 2, or t 1 = t 2. These expressions are more precise than the ones previously known.