  We examine dark matter production rates in supersymmetric axion models
typified by the mass hierarchy m_gravitino << m_neutralino << m_axino. In such
models, one expects the dark matter to be composed of an axion/gravitino
admixture. After presenting motivation for how such a mass hierarchy might
arise, we examine dark matter production in the SUSY
Kim-Shifman-Vainshtein-Zakharov (KSVZ) model, the SUSY
Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) model and a hybrid model containing
contributions from both KSVZ and DFSZ. Gravitinos can be produced thermally and
also non-thermally from axino, saxion or neutralino decay. We obtain upper
bounds on T_R due to overproduction of gravitinos including both the thermal
and non-thermal processes. For T_R near the upper bound, then dark matter tends
to be gravitino dominated, but for T_R well below the upper bounds, then axion
domination is more typical although in many cases we find a comparable mixture
of both axions and gravitinos. In this class of models, we ultimately expect
detection of relic axions but no WIMP signal, although SUSY should ultimately
be discovered at colliders.
