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Ultra-peripheral collisions (UPCs) of heavy ions involve electromagnetic interactions at large impact parameters. The large flux of photons generated by the coherent action of the proton charges generates a large flux of photons, which can be used for high-energy photoproduction studies. Heavy quarkonia produced in electromagnetic interactions provide direct information on the parton distribution functions in the nucleus at very low values of Bjorken-x. The wide pseudorapidity coverage of the CMS detectors is used to separate such events, characterized by low hadron multiplicties, from very peripheral nuclear interactions. The CMS experiment has excellent capabilities for the measurement of the heavy vector mesons in the dimuon decay channel using the tracker and the muon chambers. Using the lead-lead ion collisions data collected in 2011 and proton-lead ion collision data collected in 2013 capabilities of the CMS experiment for measuring J/psi and the photon-photon processes in ultra-peripheral collisions are shown. The prospects for future measurements using the data to be collected in the 2015 PbPb run is described.