We consider alternative superalgebras that contain some central simple alternative superalgebras of finite dimension. We prove that the classical Kronecker Factorization Theorem of Kaplansky-Jacobson is valid in arbitrary characteristic, that is, we describe the alternative algebras that contain the Cayley-Dickson algebra O. We generalize this result and prove a Kronecker Factorization Theorem for alternative superalgebras whose even part contains O. In addition, we prove a Kronecker Factorization Theorem for alternative superalgebras that contain the associative superalgebra M (1|1) (F). As a corollary of this result, we respond to an analogue of Jacobson's problem for alternative superalgebras, that is, we describe the alternative superalgebras that contain the associative superalgebra M (1|1) (F). Finally, we study the representations of the simple alternative superalgebras O(4|4) and O[u]. We classify the bimodules over these superalgebras and prove some analogues of the Kronecker Factorization Theorem for alternative superalgebras that contain O(4|4) or O[u].