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Abstract. Let Sl(G) be a Segal algebra on a locally compact group. The central functions of S '(G) are dense in the center of L\G). S\G) has central approximate units iff G G [SIN]. This is a generalization of a result of Reiter on the one hand and of Mosak on the other hand. The proofs depend on the structure theorems of [S/JV]-and [W]-groups. In the second part some new examples of Segal algebras are constructed. A locally compact group is discrete or Abelian iff every Segal algebra is rightinvariant. As opposed to the results, the proofs are not quite obvious.

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