This paper studies the structure of the set of steady state equilibria defined in quite generalized von Neumann economic models. First, it is shown that in any von Neumann production economy, there exists an admissible domain of non-negative interest rates such that for every interest rate within the domain, there exists an associated steady state equilibrium. Second, for almost all interest rates within the domain, the associated steady state equilibrium is indeterminate. Thus, in summary, for any von Neumann production economy, there is a dense subset of the admissible domain over which the set of steady state equilibria consists of a finite number of one-dimensional continuums of those equilibria. This property is observed regardless of whether the underlying economy is regular or not, which contrasts sharply with the finite and discrete properties of the other types of Walrasian equilibria in both static and intertemporal regular economies. These main results suggest, as a new, future research agenda, the need to study an appropriate equilibrium selection mechanism that should be applied prior to market competition.