The first underground data run of the ZEPLIN-II experiment has set a limit on the nuclear recoil rate in the two-phase xenon detector for direct dark matter searches .
In this paper the results from this run are converted into the limits on spin-dependent WIMP-proton and WIMP-neutron cross-sections .
The minimum of the curve for WIMP-neutron cross-section corresponds to 7 \times 10 ^ { -2 } pb at a WIMP mass of around 65 GeV .