At sufficiently large proton energies, Glauber multiple-scattering theory offers good opportunities for describing the final state interactions in electro-induced proton emission off nuclear targets. A fully unfactorized relativistic formulation of Glauber multiple-scattering theory is presented. The effect of truncating the Glauber multiple-scattering series is discussed. Relativistic effects in the description of the final-state interactions are found not to exceed the few percent level. Also the frequently adopted approximation of replacing the wave functions for the individual scattering nucleons by some average density, is observed to have a minor impact on the results when obtained in the independent-particle model. Predictions for the separated He-4(e,e'p) response functions are given in quasi-elastic kinematics and a domain corresponding with 1 less than or equal to Q(2) less than or equal to 2 (GeV)(2). (C) 2003 Elsevier B.V. All rights reserved.