The interplay of messenger RNA (mRNA), protein, produced via translation of this RNA, and nonprotein coding RNA (ncRNA) may include regulation of the ncRNA production by protein and (i) ncRNA–protein association resulting in suppression of the protein regulatory activity or (ii) ncRNA–mRNA association resulting in degradation of the miRNA–mRNA complex. The kinetic models describing these two scenarios are found to predict bistability provided that protein suppresses the ncRNA formation.