Let \(G\) be a metrizable locally compact groupoid and let \(K\) be a compact subgroup in the group \(\operatorname{Aut}(G)\) of automorphisms of \(G\). In the present paper the authors give some characterizations of a groupoid Gelfand pair which generalize some results of C. Benson, J. Jenkins and G. Ratcliff [Trans. Am. Math. Soc. 321, No. 1, 85–116 (1990; Zbl 0704.22006)].