OVER THE PAST THIRTY YEARS OR SO, the problem of the stability of a competitive general equilibrium system has been extensively studied by many economists. The first efforts at formulating the problem date back to Hicks [10], though it is well known that his analysis was purely static in nature. Taking off from Hicks' work, a number of authors (e.g., Samuelson [18], Metzler [14]) considered the dynamic stability of a linearized general equilibrium system and related their stability conditions to those obtained by Hicks. More recently, the stability of nonlinear general equilibrium systems has received a good deal of attention, and this more modern treatment originated primarily with the work of Arrow and Hurwicz [1].1 While these works indicate very clearly that major advances have been achieved in the study of stability, they all suffer from one serious defect in that they do not permit stochastic elements to be present. Therefore, the objective of the present paper is to introduce random shocks into a general equilibrium model and to investigate the resulting stability properties of such a system. This is obviously an important extension of the theory since random disturbances can enter the system in a number of ways, and in doing so possibly introduce destabilizing elements. For example, both the supply and demand functions may be subject to random shifts both in position and slope due to unforeseen exogenous factors such as changes in taste or technological uncertainties. Alternatively, the random element may be introduced because the process tatonnment which describes the adjustment to equilibrium (to be described presently) does not hold exactly. We shall interpret our results from both these standpoints. When confronted with the task of making choices in a world which is both dynamic and stochastic, individual decision makers will tend to base their behavior not only on current values of relevant variables, but also on their expected future values. For example, their expectations concerning future price movements are likely to be a very important determinant of their actions during the current period, since they will indicate how desirable it is to make a particular purchase now rather than later. Furthermore, since the current price is only a short run market equilibrium, it is quite likely to change in response to random disturbances and cannot be relied upon to provide accurate information about what future equilibrium prices are likely to be. Hence we shall assume that the excess demand functions (to be introduced in Section 2) depend on both current and expected future prices. In