This paper describes how static task-scheduling methods using stochastic search techniques can be applied to digital systems that are composed entirely of reconfigurable hardware. Such reconfigurable hardware is characterized by the property that its low-level logical functionality is not determined at the time of manufacture, but rather that this functionality becomes set only shortly before or during the invocation of the targeted application. The purpose of this paper is to introduce the basic framework for applying static scheduling theory to arbitrarily-structured task systems targeted to be implemented in prefabricated resource-constrained reconfigurable hardware. The paper also describes initial solutions to this heterogeneous task-scheduling problem that combine a distributed list-based scheduling technique with three probabilistic search strategies. The techniques introduced produce detailed task scheduling and high-level hardware configuration information that can serve as inputs to the software and reconfigurable hardware design automation tools used in the hardware/software codesign process.