For a prime p, this paper studies the hulls of separable double cyclic codes over the ring \({\mathbb {Z}}_{p^2}\) of length \(n_1+n_2\) , where \(\gcd (n_1n_2,p) = 1\) . We obtain the form of the generators of the hulls and for a given separable double cyclic code, we figure out all the separable double cyclic codes whose hulls are equal to that particular code. Further, we present some necessary and sufficient conditions for the separable double cyclic codes to be LCD, self-orthogonal, and dual-containing, respectively. Besides, we find the types, the p-dimensions, and the average p-dimensions of the hulls of separable double cyclic codes. Moreover, for a fixed p-dimension, we count the number of separable double cyclic codes whose hulls have p-dimension equal to the fixed value. Also, we have calculated the types of the hulls of these codes over \({\mathbb {Z}}_4\) and \({\mathbb {Z}}_9\) , and the average dimensions of the hulls over \({\mathbb {Z}}_9\) and \({\mathbb {Z}}_{25}\) .
