  We consider exclusive $pp \to pp \pi^{+} \pi^{-}$ and $pp \to pp \pi^{+}
\pi^{-}\pi^{+} \pi^{-}$ reactions at high energies. The calculation is based on
a tensor pomeron model and the amplitudes for the processes are formulated in
an effective field-theoretic approach. In the case of $pp \to pp \pi^{+}
\pi^{-}$ process we consider both diffractive and photoproduction mechanisms
and we include the non-resonant $\pi^{+}\pi^{-}$ continuum and the resonance
$f_{0}(500)$, $f_{0}(980)$, $f_{2}(1270)$, $\rho(770)$ contributions. We
discuss how two pomerons couple to tensor meson $f_{2}(1270)$ and the
interference effects of resonance and dipion continuum. We find that the
relative contribution of resonances $\rho(770)$, $f_2(1270)$ and dipion
continuum strongly depends on the cut on proton transverse momenta. In the case
of exclusive central $4 \pi$ production we include the contribution via the
intermediate $\sigma\sigma$ and $\rho\rho$ states. For both processes the
theoretical results have been compared with the experimental data and
predictions for planned or being carried out experiments (e.g. STAR,
ATLAS-ALFA) are presented.
