The extended Alexander group of an oriented virtual link l of d components is defined. From its abelianization a sequence of polynomial invariants ∆i(u1, . . . , ud, v), i = 0, 1, . . . , is obtained. When l is a classical link, ∆i reduces to the well-known ith Alexander polynomial of the link in the d variables u1v, . . . , udv; in particular, ∆0 vanishes.