We introduce our project on galaxy evolution in the environment of rich clusters aiming at disentangling the importance of specific interaction and galaxy transformation processes from the hierarchical evolution of galaxies in the field. Emphasis is laid on the examination of the internal kinematics of disk galaxies through spatially resolved MOS spectroscopy with FORS at the VLT. First results are presented for the clusters MS1008.1-1224 (z=0.30), Cl0303+1706 (z=0.42), and Cl0413-6559

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... TC) (z=0.51). Out of 30 cluster members with emission-lines, 13 galaxies exhibit a rotation curve of the universal form rising in the inner region and passing over into a flat part. The other members have either intrinsically peculiar kinematics (4), or too strong geometric distortions (9) or too low S/N (4 galaxies) for a reliable classification of their velocity profiles. The 13 cluster galaxies for which a maximum rotation velocity could be derived are distributed in the Tully--Fisher diagram very similar to field galaxies from the FORS Deep Field that have corresponding redshifts and do not show any significant luminosity evolution with respect to local samples. The same is true for seven galaxies observed in the cluster fields that turned out not to be members. The mass-to-light ratios of the 13 TF cluster spirals cover the same range as the distant field population indicating that their stellar populations were not dramatically changed by possible clusterspecific interaction phenomena. The cluster members with distorted kinematics may be subject to interaction processes but it is impossible to determine whether these processes also lead to changes in the overall luminosity of their stellar populations.