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This paper proposes a set of extensions to the OpenMP programming model to express complex pipelined computations. This is accomplished by defining, in the form of directives, precedence relations among the tasks originated from work-sharing constructs. The proposal is based on the definition of a name space that identifies the work parceled out by these work-sharing constructs. Then the programmer defines the precedence relations using this name space. This relieves the programmer from the burden of defining complex synchronization data structures and the insertion of explicit synchronization actions in the program that make the program difficult to understand and maintain. This work is transparently done by the compiler with the support of the OpenMP runtime library. The proposal is motivated and evaluated with a synthetic multi-block example. The paper also includes a description of the compiler and runtime support in the framework of the NanosCompiler for OpenMP.