GPU acceleration is a promising approach to speed up query processing of database systems by using low cost graphic processors as coprocessors. Two major trends have emerged in this area: (1) The development of frameworks for scheduling tasks in heterogeneous CPU/GPU platforms, which is mainly in the context of coprocessing for applications and does not consider specifics of database-query processing and optimization.(2) The acceleration of database operations using efficient GPU algorithms, which typically cannot be applied easily on other database systems, because of their analytical-algorithm-specific cost models. One major challenge is how to combine traditional database query processing with GPU coprocessing techniques and efficient database operation scheduling in a GPU-aware query optimizer. In this thesis, we develop a hybrid query processing engine, which extends the traditional physical optimization process to generate hybrid query plans and to perform a cost-based optimization in a way that the advantages of CPUs and GPUs are combined. Furthermore, we aim at a portable solution between different GPU-accelerated database management systems to maximize applicability. Preliminary results indicate great potential. algorithm is not necessarily faster than its CPU counterpart, because data has to be copied from the CPU's mainmemory to the GPU's device-memory to be processable by the GPU. Hence, these copy operations introduce a significant overhead and may lead to a slow down in system performance [16]. Therefore, it is important to use the GPU only, when it is beneficial for query processing. To this end, the query optimizer has to be aware of the properties of different processing devices, such as CPU and GPU, and has to make suitable scheduling decisions to maximize system performance [7].