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It is shown that differential Doppler shift of different patches of the blastwave front in the fireball model at varying angles to the line of sight could provide an intrinsic smoothing mechanism for the spectra of gamma-ray bursts (GRBs) and the associated afterglows at lower energy bands. For the model parameters of interest, it is illustrated that a monochromatic spectrum at ν in blastwave comoving frame is smoothed and observed to have a half-width-half-maximum (HWHM) of ∼ (0.6-2.0)ν. Somedoi:10.1086/312034 fatcat:y7i32isiuvfw5hkeo6vurp3dpy