Phylogenetic tests of adaptive evolution, such as the widely used branch-site test (BST), assume that nucleotide substitutions occur singly and independently. Recent research has shown that errors at adjacent sites often occur during DNA replication, and the resulting multinucleotide mutations (MNMs) are overwhelmingly likely to be non-synonymous. To evaluate whether the BST misinterprets sequence patterns produced by MNMs as false support for positive selection, we analysed two genome-scale datasets-one from mammals and one from flies. We found that codons with multiple differences account for virtually all the support for lineage-specific positive selection in the BST. Simulations under conditions derived from these alignments but without positive selection show that realistic rates of MNMs cause a strong and systematic bias towards false inferences of selection. This bias is sufficient under empirically derived conditions to produce false positive inferences as often as the BST infers positive selection from the empirical data. Although some genes with BST-positive results may have evolved adaptively, the test cannot distinguish sequence patterns produced by authentic positive selection from those caused by neutral fixation of MNMs. Many published inferences of adaptive evolution using this technique may therefore be artefacts of model violation caused by unincorporated neutral mutational processes. We introduce a model that incorporates MNMs and may help to ameliorate this bias.