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The influence of highly cited papers on field normalised indicatorsField normalised average citation indicators are widely used to compare countries, universities and research groups. The most common variant, the Mean Normalised Citation Score (MNCS), is known to be sensitive to individual highly cited articles but the extent to which this is true for a log-based alternative, the Mean Normalised Log Citation Score (MNLCS), is unknown. This article investigates country-level highly cited outliers for MNLCS and MNCS for all Scopus articles from 2013 and 2012. The results show that MNLCS is influenced by outliers, as measured by kurtosis, but at a much lower level than MNCS. The largest outliers were affected by the journal classifications, with the Science-Metrix scheme producing much weaker outliers than the internal Scopus scheme. The high Scopus outliers were mainly due to uncitable articles reducing the average in some humanities categories. Although outliers have a numerically small influence on the outcome for individual countries, changing indicator or classification scheme influences the results enough to affect policy conclusions drawn from them. Future field normalised calculations should therefore explicitly address the influence of outliers in their methods and reporting.