N-Methylation of DNA/RNA bases can be regulatory or damaging and is linked to diseases including cancer and genetic disorders. Bacterial AlkB and human FTO are DNA/RNA demethylases belonging to the Fe(ii) and 2-oxoglutarate oxygenase superfamily. Modelling studies reveal conformational dynamics influence structure-function relationships of AlkB and FTO, e.g. why 1-methyladenine is a better substrate for AlkB than 6-methyladenine. Simulations show that the flexibility of the double stranded DNA substrate in AlkB influences correlated motions, including between the core jelly-roll fold and an active site loop involved in substrate binding. The FTO N- and C-terminal domains move in respect to one another in a manner likely important for substrate binding. Substitutions, including clinically observed ones, influencing catalysis contribute to the network of correlated motions in AlkB and FTO. Overall, the calculations highlight the importance of the overall protein environment and its flexibility to the geometry of the reactant complexes.