Central hypergroups have been studied by Ross [21 ] (in the commutative case) and by Hauenschild et al. [11 ]. The first purpose of this paper is to complete and improve some of the results in [11 ]. Secondly, we are concerned with spectral synthesis in central hypergroups. The basic development of harmonic analysis for hypergroups can be found in [3, 7, 16, 22, 23]. In Sect. 1 we prove that the dimension function ~--*d o from the dual space /~ofa central hypergroup Kinto N is continuous and that /~ is a locally compact Hausdorff space. We use this result to define a Plancherel meausre on/~. This measure leads to a simple formulation of the Plancherel theorem and the Inversion formula for central hypergroups [11 ] (and hence also for central groups [8, 9]). Section 2 contains some results on the convolution algebra LI(K). After establishing that Kis polynomially growing we show that L ~ (K) is symmetric. Using Dixmier's functional calculus, we prove that LI(K) is completely regular. Some results on spectral synthesis are given in Sect. 3. As the main result we prove a projection theorem for central hypergroups. Let r be the canonical mapping f rom/s onto 2. Then a closed subset F of 2 is spectral if and only if its inverse image r a (F) is a spectral set. Finally, we show that the L~-kernel ker 0 contains bounded approximate units for all Q of/~.