Summary: Let \(\mathbb{P}\) be the set of all primes. A subgroup \(H\) of a group \(G\) is called \(\mathbb{P}\)-subnormal in \(G\), if either \(H = G\), or there exists a chain of subgroups \[ H=H_0 \leqslant H_1 \leqslant \dots \leqslant H_n=G, \] with \(|H_i:H_{i-1}| \in \mathbb{P}\) for all \(i\). A group \(G=AB\) with \(\mathbb{P}\)-subnormal supersoluble subgroups \(A\) and \(B\) is studied. The structure of its supersoluble residual is obtained. In particular, it coincides with the nilpotent residual of the derived subgroup of \(G\). Besides, if the indices of the subgroups \(A\) and \(B\) are coprime, then the supersoluble residual coincides with the intersection of the metanilpotent residual of \(G\) and all normal subgroups of \(G\) such that all corresponding quotients are primary or biprimary. From here new signs of supersolubility are derived.