  We analyse the direct detection of neutralino dark matter in the framework of
the Next-to-Minimal Supersymmetric Standard Model. After performing a detailed
analysis of the parameter space, taking into account all the available
constraints from LEPII, we compute the neutralino-nucleon cross section, and
compare the results with the sensitivity of detectors. We find that sizable
values for the detection cross section, within the reach of dark matter
detectors, are attainable in this framework. For example, neutralino-proton
cross sections compatible with the sensitivity of present experiments can be
obtained due to the exchange of very light Higgses with $m_{h_1^0}\lsim 70$
GeV. Such Higgses have a significant singlet composition, thus escaping
detection and being in agreement with accelerator data. The lightest neutralino
in these cases exhibits a large singlino-Higgsino composition, and a mass in
the range $50\lsim m_{\tilde\chi_1^0}\lsim 100$ GeV.
