Abstract Interferon superinduction, in the case of cell pretreatment with low doses of interferon (priming), may be explained by activation of 2′,5′-oligoadenylate synthetase and endonuclease L, since the latter, as expected, leads to a more rapid amplification of the standard scheme of interferon induction based on the antirepression mechanism. In the given case, endonuclease L will further increase the degradation rates for messages, which encode repressor proteins controlling interferon gene expression. Under ordinary induction, these messages are destroyed only by short-lived nuclease activated by double-stranded RNA. Cell pretreatment with high doses of interferon (blocking) considerably increases the concentrations of protein kinase and 2′,5′-oligoadenylate synthetase in the cell. However, it seems that during blocking protein kinase plays the main role in inhibition of interferon synthesis, and this leads to almost complete depression of translation in the cell. When protein kinase is not sufficiently activated, blocking does not occur since treatment of cells with high concentrations of interferon does not hinder priming induced by 2′,5′-oligoadenylate synthetase and endonuclease L. The proposed model is consistent with the findings that both interferon-treated primed and blocked cells are able to produce interferon more rapidly than normal cells. The analysis, based on a computer simulation model, suggests that priming and blocking of interferon may be based on processes controlling its induction and antiviral activity.