  We present a study of the exclusive production of meson pairs in the
four-body $pp \to pp \pi^{+} \pi^{-}$, $pp K^{+}K^{-}$ reactions at high
energies which constitute an irreducible background to resonance states (e.g.
$\phi$, $f_{2}(1270)$, $f_{0}(1500)$, $f_{2}'(1525)$, $\chi_{c0}$). We consider
central diffractive contribution mediated by Pomeron and Reggeon exchanges and
new diffractive mechanism of emission of pions/kaons from the proton lines. We
include absorption effects due to proton-proton interaction and pion/kaon
rescattering. Predictions for the total cross section and differential
distributions in pion/kaon rapidity and transverse momentum as well as
two-pion/kaon invariant mass are presented for the RHIC, Tevatron and LHC
colliders. Finally we consider a measurement of exclusive production of a
scalar $\chi_{c0}$ meson via $\chi_{c0} \to \pi^{+} \pi^{-}$, $K^{+} K^{-}$
decay.
