We have developed a system to process database queries over composed data providing web services. The queries are transformed into execution plans containing an operator that invokes any web service for given arguments. A common pattern in these query execution plans is that the output of one web service call is the input for another, etc. The challenge addressed in this paper is to develop methods to speed up such dependent calls in queries by parallelization. Since web service calls incur high-latency and message set-up costs, a na?ve approach making the calls sequentially is time consuming and parallel invocations of the web service calls should improve the speed. Our approach automatically parallelizes the web service calls by starting separate query processes, each managing a parameterized subquery, a plan function, for different parameter tuples. For a given query, the query processes are automatically arranged in a multi-level process tree where plan functions are called in para...