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.