In this paper we study the structure of the Weyl groups of nonreduced extended affine root systems. We show that similar to the case of reduced types, an extended affine Weyl group W of type BC ℓ is semidirect product of a finite Weyl group W ̇ (of type B ℓ) and a Heisenberg-like normal subgroup H which is also a characteristic subgroup of W . Moreover, H is of the form H= H η H 0 , where both H η and H 0 are normal subgroups of H with H η∩ H 0≠{1} , H η is naturally isomorphic to the root lattice of a finite root system of type BC ℓ. Furthermore, the semidirect product of W ̇ and H η is isomorphic to the Weyl group of a Kac–Moody affine subroot system of R of type BC ℓ.