The requirements of high computational performance and flexibility of the contemporary embedded systems are continuously increasing. Moreover, a single architecture must be able to support different applications with dynamical requirements (changing environments). Reconfigurable computing based on hybrid architectures, comprising general purpose processor (CPU) and Field Programmable Gate Array (FPGA), is very attractive because it can provide high computational performance as well as flexibility to support the requirements of today's embedded systems. An operating system (OS), which is desired to provide support for such systems, has to use the available resources in an optimal way (competing with the applications), since embedded system architectures are usually lacking in resources. In this paper, we present our approach towards a reconfigurable RTOS that is able to distribute itself over a hybrid architecture (comprising FPGA and CPU). We will describe the main concepts and methods used to achieve the desired RTOS. Moreover, we present some preliminary evaluation results which show the realizability of our approach.