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Exclusive and diffractive physics measurements are important for the betterunderstanding of the non-perturbative regime of QCD. Two recent results of theCMS experiment is presented in this paper. The total and differential crosssections of central exclusive $\pi^+\pi^-$ production are measured at 5.02 and13 TeV in the $p_{\mathrm{T}}(\pi) > 0.2~$GeV/$c$ and $|\eta(\pi)| < 2.4$kinematic region. The invariant mass distribution is fitted by the sum of acontinuum and four interfering relativistic Breit-Wigner functions. In thesecond part of the paper the measurement of the single diffractive dijets ispresented, which are studied by using proton tagging capabilities of the TOTEManalysis. A joint CMS-TOTEM study is carried out and the total and differentialcross sections are measured in the $0.03 < |t| < 1.0~$GeV$^2$ and $0 < \xi <0.1$ kinematic region.

Recent CMS and CMS-TOTEM results on diffraction and exclusive production