Software development kits (SDKs) and supporting tools for Graphics Processor Units (GPUs) have matured and they now enable the implementation of complex middleware that takes advantage of the additional processing power. Working in synergy with CPUs, GPUs are suitable for executing highly parallelized tasks on streams of data. In this paper, we investigate the realization of effective operations on streams of data using GPU resources. We suggest a model for computing basic SQL-like queries that include unary/binary logical operators, membership queries as well as joins based on nested-loops. We also propose a framework that exploits the above core operations to offer a generalized computing environment for managing streams of data. Through experimentation with the NVIDIA CUDA SDK, we show sizable benefits in obtaining shorter response times not only for simple operations but also for more complex queries on streams.