An important property of the epigenetics ‘marks’ and of the epigenetic phenomena in general is its stability, the ability of the cell to maintain its epigenetic state through cell division. During DNA replication this marks are bound to be diluted due to newly synthesized histone proteins indicating that this heritable states must be robust against significant fluctuations in the concentration of ‘marks’. We develop a model in order to identify necessary conditions for stability of the chromatin states, that correspond to distinct epigenetic phenotypes, taking in considerations also the effects of the fluctuations in concentration of epigenetic marks due to DNA replication and cell division.