Abstract : A search for exclusive or semi-exclusive photon pair production, pp to p* + photon pair + p(*) (where p* stands for a diffractively-dissociated proton), and the observation of exclusive and semi-exclusive electron pair production, pp to p(*) + ee + p(*), in proton-proton collisions at sqrt(s)=7 TeV, are presented. The analysis is based on a data sample corresponding to an integrated luminosity of 36 inverse picobarns recorded by the CMS experiment at the LHC at low instantaneous luminosities. Candidate photon pair or electron pair events are selected by requiring the presence of two photons or a positron and an electron, each with transverse energy ET > 5.5 GeV and pseudorapidity abs(eta) < 2.5, and no other particles in the region abs(eta) < 5.2. No exclusive or semi-exclusive diphoton candidates are found in the data. An upper limit on the cross section for the reaction pp to p(*) + photon pair + p(*), within the above kinematic selections, is set at 1.18 pb at 95% confidence level. Seventeen exclusive or semi-exclusive dielectron candidates are observed, with an estimated background of 0.85 +/- 0.28 (stat) events, in agreement with the QED-based prediction of 16.3 +/- 1.3 (syst) events.