A non-Markov theory of diffuse satellites developing around the allowed (mother) rotational lines perturbed by monoatomic buffer gases is expounded. As the buffer-gas pressure grows, the lorentzian part of mother lines adjacent to the band origin becomes attenuated because of the intensity transfer to pressure-enhanced satellites. Different channels contributing to the attenuation of infrared and Raman lines of linear molecules are considered. Simple estimations of the attenuation coefficients reasonably fit experimental data available for the HCl and HF absorption spectra perturbed by monatomic gases.