Let \(G\) be a locally compact hypergroup and let \(K\) be a compact subhypergroup of \(G\) . \((G,K)\) is a Gelfand pair if \(M_{c}(G//K)\) , the algebra of measures with compact support on the double coset \(G//K\) , is commutative for the convolution. In this paper, assuming that \((G,K)\) is a Gelfand pair, we define and study the dual and the Gelfand dual integrable representations of \(G\) and then give necessary and sufficient conditions for a representation on \(G\) to be dual or Gelfand dual integrable.
