  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 0.07 pb at a WIMP mass
of around 65 GeV.
