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Task scheduling is in general an NP-complete problem. For this reason a huge number of heuristics have been presented in the literature to obtain near optimal schedules. These heuristics mainly target homogeneous computing systems, while a few of them target heterogeneous systems. The heterogeneous heuristics presented so far target computing machines with different capabilities, while almost none of them handle heterogeneous communication systems. This paper presents a novel task scheduling algorithm called the heterogeneous critical tasks reverse duplicator (HCTRD), which targets both heterogeneous computation and communication systems. The algorithm is based on list-scheduling and task-duplication in a bounded number of machines, and aims to achieve high performance and near lower bound complexity.