Workflow applications executed in Grid environments are not able to take advantage of all the potential parallelism they might have. This limitation in the usage of parallelism comes from the fact that when there is a producer/consumer situation communicating using files, the consumer does not start its execution till the producer has finished creating the file to be consumed, and the file has been copied to the consumer (if needed). In this paper, we propose a publish/subscribe mechanism that allows consumers to read the file at the same time it is being produced. In addition, this mechanism is implemented in a transparent way to the application, so does not require any special feature from the local filesystems. Finally, we show that our mechanisms can speedup applications significantly. In our best test we divided by two the execution time of some applications, but other applications may have even higher benefits. Key words: Grid Workflow Parallelism Storage