Cells are capable of maintaining a long-term memory in addition to genetic information, which is generally referred to as epigenetics. In the study of memory, digital memory has been often assumed, which is understood as multistability, whereas in the cell there is another form of memory – continuous (analog), kinetic memory. Referring to the kinetic constraints of the glass theory, it is shown that a kinetic memory with slow relaxation emerges as an alternative to the conventional memories of multiple stable states. It is characterized by a slow logarithmic change with several plateaus that can be occupied during the relaxation process. If the same enzyme catalyzes a stepwise reaction, as long as the amount of such enzyme is not sufficient, the reaction process can be hindered by enzyme-limited competition, resulting in kinetic memory. A combination of catalytic reactions can create a negative correlation between the amount of substrate and enzyme in it, thereby allowing a slow relaxation process with many plateaus, where multiple states can be maintained over a long period of time.