Electromagnetic lepton‐pair production in relativistic collisions is studied in anab initioapproach with no free parameters. After a semi‐classical approximation to the relative motion of the two incident particles is made, the resulting second‐order diagram is calculated using a Monte Carlo technique to evaluate the resulting seven‐dimensional integral. We examine the case of electron‐positron pair production in &pgr;−pcollisions atp&pgr;=17 GeV. We find that a significant fraction of the measured pairs in this reaction are produced via the magnetic spin‐flip current of the proton. Approaches, such as the equivalent photon approximation, which neglect this part of the current predict much too small a cross section. This feature is traced to the cuts imposed in taking the experimental data. Lepton‐pair production in the scattering of3He,4He and4He,4He is proposed as a clean way of experimentally separating the spin‐flip and non‐flip processes; predictions are made for these systems.