  In this paper, we begin the study of poles of partial L-functions L^S(sigma
tensor tau,s), where sigma tensor tau is an irreducible, automorphic, cuspidal,
generic (i.e. with nontrivial Whittaker coefficient) representation of G_A x
GL_m(A). G is a split classical group and A is the adele ring of a number field
F. We also consider tilde{Sp}_{2n}(A) x GL_m(A), where tilde denotes the
metaplectic cover.
