The neutron capture cross sections of Pr-141, Dy-160, Dy-161, Dy-161, Dy-163 and Dy-164 have been measured in Be energy range from 3 to 225 keV at the Karlsruhe 3.75 MV Van de Graaff accelerator. Neutrons were produced via the Li-7(p,n)Be-7 reaction by bombarding metallic Li targets with a pulsed proton beam. Capture events were registered with the Karlsruhe 4 pi Barium Fluoride Detector. The cross sections were determined relative to the gold standard. For the first time the correction for undetected capture events was completely obtained from experimental information, using capture cascades derived from measurements with an analog-to-digital converter system. The cross section ratios could be determined with an overall uncertainty of 1-1.5 factor 4. Maxwellian averaged neutron capture cross sections were calculated for thermal energies between kT = 8 keV and 100 keV. For most of the isotopes there is reasonable agreement with recent evaluations, but discrepancies of similar to 20 Dy-160 and Dy-164. The experimental data were complemented by statistical model calculations in order to describe the cross section enhancements in the stellar environment. The astrophysical implications of the present data include the quest for the origin of Dy-160, the decomposition of the Dy abundances in the respective s- and r-process contributions, branchings of the s-process chain at the terrestrially stable isotopes Gd-157 and Dy-163, and the isotopically anomalous dysprosium in meteoritic inclusions. [S0556-2813(99)04002-9].