Methylation of DNA cytosine bases is a key epigenetic modification that plays an important role in the regulation of gene expression and the formation of the epigenome. Numerous studies of the human genome show that there is a close relationship between DNA methylation, age and sex of a person. Until now, the popular model has been the linear change in the methylation level with age. Here we find a fundamentally different DNA methylation behavior, namely the nonlinear dependence of the methylation level on age. We identify CpG probes whose methylation changes exponentially with age or according to a power law, and perform Gene Ontology enrichment analysis of the latter. Our results are relevant to understanding how DNA methylation changes with age and the found nonlinear CpG sites can be used to construct new epigenetic clocks.