The very strong electromagnetic fields present in ultraperipheral relativistic heavy ion collisions lead to important higher order effects of the electromagnetic interaction. These multiphoton exchange processes are studied using perturbation theory and the sudden or Glauber approximation. In many important cases, the multi-photon amplitudes factorize into independent single-photon amplitudes. These amplitudes have a common impact parameter vector, which induces correlations between the amplitudes. Impact-parameter dependent equivalent-photon spectra for simultaneous excitation are calculated, as well as, impact-parameter dependent gammagamma-luminosities. Excitations, like the multiphonon giant dipole resonances, vector meson production and multiple e+e- pair production can be treated analytically in a bosonic model, analogous to the emission of soft photons in QED.
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