Viral genomes are often extremely compact. Revealing the factors that drive the composition of these genomes is central to understanding viral evolution. Surprisingly, substantial biases in nucleotide composition exist for many viruses. For example, many viruses are particularly āAā-rich. One potential explanation lies in cellular enzymes that combat viral infection, such as the APOBEC3 family of enzymes whose activity results in substitution of G>A in DNA genomes of viruses. Similar host factors that act against different viral groups have not been yet identified. Here, we searched for evidence of novel factors that act against viruses and potentially lead to biases in viral genomic composition. To this end, we began by analyzing a wide dataset of viral alignments spanning a variety of viral families and different hosts, ranging from plants to insects to vertebrates. We developed a computational pipeline to construct rooted phylogenies for each alignment, thus enabling us to analyze the data using non-reversible models of evolution. Our results reveal that there are strong biases in nucleotide substitution rates and nucleotide frequencies in several viral families. There is a preference for C>U and G>A mutations over the respective opposite mutations. Additionally, we found that there is a general preference for A nucleotide that causes many viruses to be "A"-rich and āCā-poor. We discuss the implications of these findings, which suggest that nucleotide substitution may be driven by additional cellular forces, thus altering the fitness landscape of viruses.