  Random matrix models based on an integral over supermatrices are proposed as
a natural extension of bosonic matrix models. The subtle nature of superspace
integration allows these models to have very different properties from the
analogous bosonic models. Two choices of integration slice are investigated.
One leads to a perturbative structure which is reminiscent of, and perhaps
identical to, the usual Hermitian matrix models. Another leads to an eigenvalue
reduction which can be described by a two component plasma in one dimension. A
stationary point of the model is described.
