[en] At the planned International Linear Collider (ILC), the longitudinal beam polarization needs to be determined with an unprecedented precision. For that purpose, the beam delivery systems (BDS) are equipped with two laser Compton polarimeters each, which are foreseen to achieve a systematic uncertainty of ≤ 0.25 %. The polarimeters are located 1.6 km upstream and 150 m downstream of the e⁺e^- interaction point (IP). The average luminosity-weighted longitudinal polarization P^lumi_z, which is the decisive quantity for the experiments, has to be determined from these measurements with the best possible precision. Therefore, a detailed understanding of the spin transport in the BDS is mandatory to estimate how precise the longitudinal polarization at the IP is known from the polarimeter measurements. The envisaged precision for the propagation of the measurement value is ≤ 0.1 %. This thesis scrutinizes the spin transport in view of the achievable precision. A detailed beamline simulation for the BDS has been developed, including the simulation of the beam-beam collisions at the IP. The following factors which might limit the achievable precision is investigated: a variation of the beam parameters, the beam alignment precision at the polarimeters and the IP, the bunch rotation at the IP, the detector magnets, the beam-beam collisions, the emission of synchrotron radiation and misalignments of the beamline elements. In absence of collisions, a precision of 0.085% on the propagation of the measured longitudinal polarization has been found achievable. This result however depends mainly on the presumed precisions for the parallel alignment of the beam at the polarimeters and for the alignment of polarization vector. In presence of collisions, the measurement at the downstream polarimeter depends strongly on the intensity of the collision and the size of the polarimeter laser spot. Therefore, a more detailed study of the laser-bunch interaction is required for a quantitative statement.