The oscillating two stream instability (OTSI) of a high amplitude laser or a plasma wave in near-critical density high-Z plasma is influenced by the presence of light ions. A regime of OTSI arises where the low frequency response of electrons and light ions is adiabatic but the heavy ion response is much slower. As a consequence the low frequency mode is not a purely growing mode but has a finite real frequency as well. In the case of a pump, radially localized in a suitable density profile, the growth rate is reduced and the wavelength of the maximally growing mode is enhanced.