We present our project on galaxy evolution in the environment of distant rich clusters aiming at disentangling the importance of specific interaction and galaxy transformation processes from the hierarchical evolution of field galaxies. Spatially resolved MOS spectra were gained with VLT/FORS to analyze the internal kinematics of disk galaxies. First results are shown for the clusters MS 1008.1–1224 ($z=0.30$), Cl 0303+1706 ($z=0.42$), and Cl 0413–6559 ($z=0.51$). Out of 35 late-type cluster members, 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 peculiar kinematics. The 13 cluster galaxies for which a maximum rotation velocity could be derived are distributed in the Tully-Fisher diagram very similarly to field galaxies from the FORS Deep Field with corresponding redshifts. The same is true for seven non-cluster galaxies observed in the cluster fields. The TF-cluster spirals do not show any significant luminosity evolution as might be expected from certain phenomena specific to clusters. Contrary to that, the disturbed kinematics of the non–TF cluster spirals indicate ongoing or recent interaction processes.