Most Type II supernovae probably have red supergiant progenitor stars which are expected to have slow, dense winds; multiwavelength observations of some Type II supernovae show evidence for interaction of the supernova with the wind. Recent optical spectroscopy of some normal supernovae at ages of approximately 10 yr or more has shown emission lines such as Halpha, [O I], and [O III]. We investigate the circumstellar interaction model for this emission, beginning with the hydrodynamics of the interaction. An early cooling phase is expected at the reverse shock front and the dense shell that it is built up can play a dominant role in the absorption of X-rays produced at the shock front. A steep supernova density gradient gives rise to a relatively slow reverse shock front and the reverse shock emission is at far-ultraviolet wavelengths. This radiation field produces a highly ionized region in this supernova ejecta with a sharp boundary. The reverse shock has higher temperatures for a flatter supernova density profile and gives an X-ray-dominated spectrum. In this case, there is a heated broad inner region in the supernova ejecta with low ionization. In both cases, radiation from the shock front can be absorbed by the shell formed by radiative cooling, giving rise to a low-ionization spectrum. Thus, high-ionization lines are formed in the freely expanding supernova ejecta, while low-ionization lines are formed both in the ejecta and in the shocked shell. We compare the models to observations of SN 1980K and SN 1979C up to an age of 10 yr and find that the models with a relatively flat power law profile and X-ray heating show good agreement with the strongest optical lines. The models predict an increase of the [O III]/Halpha ratio at late times because of a decrease in collisional deexcitation of the [O III]; such a large ratio has been recently observed in SN 1957D. We also make predictions of the strongest ultraviolet and infrared lines to be expected from circumstellar interaction.