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We analyse the direct detection of neutralino dark matter in the framework ofthe Next-to-Minimal Supersymmetric Standard Model. After performing a detailedanalysis of the parameter space, taking into account all the availableconstraints from LEPII, we compute the neutralino-nucleon cross section, andcompare the results with the sensitivity of detectors. We find that sizablevalues for the detection cross section, within the reach of dark matterdetectors, are attainable in this framework. For example, neutralino-protoncross sections compatible with the sensitivity of present experiments can beobtained due to the exchange of very light Higgses with $m_{h_1^0}\lsim 70$GeV. Such Higgses have a significant singlet composition, thus escapingdetection and being in agreement with accelerator data. The lightest neutralinoin these cases exhibits a large singlino-Higgsino composition, and a mass inthe range $50\lsim m_{\tilde\chi_1^0}\lsim 100$ GeV.Comment: Final version to appear in JHEP. References added. LaTeX, 53 pages,  23 figure

Theoretical predictions for the direct detection of neutralino dark matter in the NMSSM