We present here the second in a sequence of three papers devoted to the Gromov-Witten theory of nonsingular target curves X. Let ω ∈ H2(X,Q) denote the Poincar´e dual of the point class. In the first paper , we considered the stationary sector of the Gromov-Witten theory of X formed by the descendents of ω. The stationary sector was identified in  with the Hurwitz theory of X with completed cycle insertions. The target P1 plays a distinguished role in the Gromov-Witten theory of target curves. Since P1 admits a C∗-action, equivariant localization may be used to study Gromov-Witten invariants . The equivariant Poincar´e duals,.