 Existence of instanton singularities is beyond any doubt, while existence of renormalon ones was never proved rigorously in spite of numerous efforts.Among the essential contributions one should mention the application of the operator product expansion, as was suggested by Parisi.Recently a proof was suggested for absence of renormalon singularities in formula_10 theory and a general criterion for their existence was formulated in terms of the asymptotic behavior of the Gell-Mann - Low function formula_11.