A model describing the main processes determining the evolution of hydrocarbon dust grains of arbitrary size under astrophysical conditions corresponding to regions of ionized hydrogen (HII regions) and supernova remnants is presented. The processes considered include aromatization and photodestruction, sputtering by electrons and ions, and shattering during collisions between grains. The model can be used to calculate the size distribution of the grains and the degree of aromatization during the evolution of HII regions and supernova remnants for a specified radiation field, relative velocity between the gas and dust, etc. The contribution of various processes to the evolution of hydrocarbon dust grains for parameters typical for the interstellar medium of our Galaxy is considered. Small grains (with fewer than 50 carbon atoms) should be fully aromatized in the interstellar medium. If larger grains initially have an aliphatic structure, this is preserved to a substantial extent. Variation in the size distribution of the grains due to collisions between grains depend appreciably on the adopted initial size distribution. With an initial distribution corresponding to that of Mathis et al. (1977), the mass fraction contributed by smaller grains tends to increase with time, while, with an initial distribution corresponding to that of Jones et al. (2013), in which the fraction of small grains is initially high, there is a general decrease in the number of grains of various sizes with time.