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Phylogenetic analysis has become essential in researching the evolutionary relationships between viruses. These relationships are depicted on phylogenetic trees, in which viruses are grouped based on sequence similarity. Viral evolutionary relationships are identified from open reading frames rather than from complete sequences. Recently, cloud computing has become popular for developing internet-based bioinformatics tools. Biocloud is an efficient, scalable, and robust bioinformatics computing service. In this paper, we propose a cloud-based open reading frame phylogenetic analysis service. The proposed service integrates the Hadoop framework, virtualization technology, and phylogenetic analysis methods to provide a high-availability, large-scale bioservice. In a case study, we analyze the phylogenetic relationships among Norovirus. Evolutionary relationships are elucidated by aligning different open reading frame sequences. The proposed platform correctly identifies the evolutionary relationships between members of Norovirus.