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We calculate the one-loop induced couplings of two gaugino-like neutralinosto the $Z$ and Higgs bosons in the Minimal Supersymmetric Standard Model. Thesecouplings, which vanish at the tree level, can be generated through loopsinvolving fermions and sfermions. We show that, while the neutralinocontribution to the invisible $Z$ boson decay width remains small, the loopinduced couplings to the lightest Higgs boson might be sufficiently large toyield a rate of invisible decays of this Higgs boson that should be detectableat future $e^+e^-$ colliders. We also study the implications of these couplingsfor direct searches of Dark Matter and show that they can modify appreciablythe neutralino-nucleon elastic cross section for some parameter range.Comment: LaTeX with 6 (e)ps and 2 axodraw figures, 25 pages in total;  axodraw.sty is included v.2: Added one figure and some discussions; version  to appear in PR

Loop induced Higgs andZboson couplings to neutralinos and implications for collider and dark matter searches