  We discuss processes leading to two photon final states in peripheral heavy
ion collisions at RHIC. Due to the large photon luminosity we show that the
continuum subprocess $\gamma \gamma \to \gamma \gamma$ can be observed with a
large number of events. We study this reaction when it is intermediated by a
resonance made of quarks or gluons and discuss its interplay with the continuum
process, verifying that in several cases the resonant process ovewhelms the
continuum one. It is also investigated the possibility of observing a scalar
resonance (the $\sigma$ meson) in this process. Assuming for the $\sigma$ the
mass and total decay width values recently reported by the E791 Collaboration
we show that RHIC may detect this particle in its two photon decay mode if its
partial photonic decay width is of the order of the ones discussed in the
literature.
