During the course of a lifetime, somatic cells acquire mutations. Different mutational processes may contribute to the mutations accumulated in a cell, with each imprinting a mutational signature on the cell's genome. Some processes generate mutations throughout life at a constant rate in all individuals, and the number of mutations in a cell attributable to these processes will be proportional to the chronological age of the person. Using mutations from 10,250 cancer genomes across 36 cancer types, we investigated clock-like mutational processes that have been operating in normal human cells. Two mutational signatures show clock-like properties. Both exhibit different mutation rates in different tissues. However, their mutation rates are not correlated, indicating that the underlying processes are subject to different biological influences. For one signature, the rate of cell division may influence its mutation rate. This study provides the first survey of clock-like mutational processes operating in human somatic cells.