In this paper it is constructed a new grand grand Sobolev-Morrey $S_{p),\varkappa ),a,\alpha }^{l}W(G)$ spaces with dominant mixed derivatives. With help integral representation of generalized mixed derivatives of functions, defined on $n$-dimensional domains satisfying flexible horn condition, an embedding theorem is proved. In other works, the embedding theorem is proved in these spaces and belonging of the generalized mixed derivatives of functions from these spaces to the Holder class, was studied.