Recently a proof was suggested for absence of renormalon singularities in ϕ ϕ 4 theory and a general criterion for their existence was formulated in terms of the asymptotic behavior of the Gell-Mann–Low function β β ( g ) . Analytical results for asymptotics of β β ( g ) in ϕ ϕ 4 theory and QED indicate the absence of renormalon singularities in these theories.