Encapsulating parallelism and synchronization code within object-oriented software components is a promising avenue towards mastering the complexity of the distributed memory supercomputer programming. However, in trying to give application programmers benefit of supercomputer power, the library designer generally resorts to low level parallel constructs, a time consuming and error prone process. To solve this problem we introduce a new abstraction called Parallel Operators. A Parallel Operator exists simultaneously on all processors involved in a distributed computation: it acts as a single entity capable of processing shared or distributed data in parallel. In this paper we reify this concept in our Eiffel Parallel Execution Environment (EPEE) context, and we show that it is both natural and efficient to express computations over large shared or distributed data structures using Parallel Operators. We illustrate our approach with an Parallel Operator based solution for the well-known N-body problem.