It is proved that for a class of nonlocal potentials, the S matrix element S(λ,k) as a function of the angular momentum λ is meromorphic in λ in the region Re λ > 0. It is proved further that as λ→∞ along the positive real axis or the negative imaginary axis, S(λ, k)-1 exp(-iπλ)→0. Under more restrictive assumptions, it is shown that S(λ, k) is meromorphic with respect to the momentum variable k in the strip |Im k| < μ. The positions of the poles are discussed. For such potentials, the Regge poles in the right half plane do not lie necessarily in the first quadrant.