[en] In recent experiments at the SPS, and in the near future colliding-beam accelerators, such as RHIC and LHC, peripheral heavy-ions collisions produce strong, Lorentz contracted electromagnetic fields. The high charges and high energies of the ions give large cross sections for electromagnetic lepton - antilepton pair production. In this work, a non-perturbative treatment of pair production under these extreme conditions is considered. The two-center Dirac equation for an electron in the external electromagnetic field of two colliding heavy ions in the limit in which the ions are moving at the speed of light is exactly solved off the light fronts using light-front variables and a light-fronts representation. The electromagnetic fields of the ions are confined to the light fronts by the extreme Lorentz contraction and by a choice of gauge designed to incorporate the long-range Coulomb effects into the definition of the asymptotic states. After the peripheral collision, as the ions move apart, the solution in the space between them is determined by the non-trivial boundary conditions at the light fronts. An exact integral representation for the free pair creation amplitudes off the light fronts is obtained by calculating the transition currents flowing from the light fronts into the space between the separating ions. The condition for the applicability of this nonperturbative solution for large but finite collision energy is found, and used to explain recent experimental results according to which the measured production rates scale as the square of the projectile and target charges, even for large charges. It is shown that this observed scaling of positron yields is a result of an exact cancellation of a nonperturbative charge dependence. Nonperturbative effects may contribute significantly to the small-momentum-transfer regime, and to asymptotic states on the light fronts, as well as to results for multiple pair-production, and for correlations between the produced pairs