  We derive the high energy asymptotic of one- and two-loop corrections in the
next-to-next-to-leading logarithmic approximation to the differential cross
section of $W$-pair production at the LHC. For large invariant mass of the
W-pair the (negative) one-loop terms can reach more than 40%, which are
partially compensated by the (positive) two-loop terms of up to 10%.
