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Warner (1966), Hewitt and Ross (1970), Yap (1970), and Yap (1971) extended the so-called Ditkin’s condition for the group algebra L 1 (G) of a locally compact abelian group G to the algebras L 1 (G)∩ L 2 (G), dense subalgebras of L 1 (G) which are essential Banach L 1 (G)-modules, L 1 (G)∩ L p (G)(1≦ p<∞) and Segal algebras respectively. Chilana and Ross (1978) proved that the algebra L 1 (K) satisfies a stronger form of Ditkin’s condition at points of the center Z (K) of K, where K is a commutative locally compact hypergroup such that its dual K is also a hypergroup under pointwise operations. Topological hypergroups have been defined and studied by Dunkl (1973), Spector (1973), and Jewett (1975) to begin with. In this paper we define Segal algebras on K and prove that they satisfy a stronger form of Ditkin’s condition at the points of Z (K). Examples include the analogues of some Segal algebras on …