We study neutralino sectors in extensions of the MSSM that dynamically generate the A-term. The extra neutralino states are superpartners of the Higgs singlets and/or additional gauge bosons. The extended models may have distinct lightest neutralino properties which can have important influences on their phenomenology. We consider constraints on the lightest neutralino from LEP, Tevatron, and (g - 2)(mu) measurements and the relic density of the dark matter. The lightest neutralino can be extremely light and/or dominated by its singlino component which does not couple directly to SM particles except Higgs doublets. (c) 2005 Elsevier B.V. All rights reserved.