The objects studied are singular links of spheres of dimensions p ₁,..., p_r, and p in the n-sphere. A theory of such singular links for the case where max{p₁,..., p_r} < min{2n/3 - 1, n - (p + 5)/3} is constructed. The theory generalizes (as far as it is possible) the theory of singular links of spheres of dimensions k,..., k, and p in the (2k + 1)-sphere, where k > 1, developed in the author's recent papers. Bibliography: 13 titles.