  We compute the one loop contribution coming from vertex and box diagrams,
where virtual top quarks are exchanged, to the asymptotic energy behaviour of
$b\bar b$ pair production at future lepton colliders. We find that the effect
of the top mass is an extra linear logarithmic term of Sudakov type that is not
present in the case of (u,d,s,c) production. This appears to be particularly
relevant in the case of the $b\bar{b}$ cross section.
