The evolution of finite‐amplitude plane waves as they propagate through monodisperse aerosols of spherical particulate matter is investigated theoretically. Attenuation, dispersion, and the growth of higher harmonics are considered in detail. It is shown that, except for the case of very low dust‐loading, the particulate matter dominates the gas self‐viscosity in determining acoustic processes. Using a criterion based upon harmonic ratios, regimes of allowed and precluded shock‐formation are tentatively identified and, in the case of the former, shock‐formation distances are given. The shock‐formation distance in an aerosol is shown to always be greater than that of the corresponding clean‐gas case. Finally, the theory is extended to polydisperse systems. The results reduce to those of existing theories for the limiting cases of (i) infinitesimal‐amplitude acoustics of dusty gases and (ii) finite‐amplitude acoustics of clean gases.