A search for exclusive or semi-exclusive gamma gamma production, pp -> p(()*()) + gamma gamma + 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 root 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 gamma gamma 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 vertical bar eta vertical bar < 2.5, and no other particles in the region vertical bar eta vertical bar < 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(()*()) + gamma gamma + 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.