  We discuss central exclusive production of $W^+W^-$ pairs in proton-proton
collisions at LHC. Predictions for the total cross section and differential
distributions in transverse momentum of $W^{\pm}$ and $WW$ invariant mass are
presented. We discuss both $\gamma \gamma \to W^+ W^-$ mechanism as well as a
new mechanism of exclusive diffractive production. The amplitude for the latter
process is calculated in the Durham model. We compare the two (QED and QCD)
types of contributions. The diffractive contribution is only a small fraction
of fb compared to the $\gamma \gamma$ contribution which is of the order of 100
fb. This opens a possibility of searches for anomalous four-boson $\gamma
\gamma W^+ W^-$ coupling due to physics beyond Standard Model.
