A search for exclusive or semi-exclusive γγ production, pp → p() + γγ + p() (where p* stands for a diffractively-dissociated proton), and the observation of exclusive and semi-exclusive e+e− production, pp → p() + e+e− + p(), in proton-proton collisions at √s=7 TeV, are presented. The analysis is based on a data sample corresponding to an integrated luminosity of 36 pb−1 recorded by the CMS experiment at the LHC at low instantaneous luminosities. Candidate γγ or e+e− events are selected by requiring the presence of two photons or a positron and an electron, each with transverse energy E T  > 5.5 GeV and pseudorapidity |η| < 2.5, and no other particles in the region |η| < 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 → p() + γγ + 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.