We determine the poles of Eisenstein series on GL(n(m_1+m_2), A), induced from two Speh representations, based on the same irreducible cuspidal representation of GL(n,A), of "lengths" m_1, m_2, with complex parameter (s,-s), Re(s) non-negative. The poles are simple. We determine the wave front sets of their residues. Our methods, which involve, among other things, a descent operation, analogous to Bernstein-Zelevinsky derivatives, also show that when m_1=m_2, the above Eisenstein series vanish at s=0. This is a joint work with David Ginzburg.