  The complex Langevin method is a general method to treat systems with complex
action, such as QCD at nonzero density. The formal justification relies on the
absence of certain boundary terms, both at infinity and at the unavoidable
poles of the drift force. Here I focus on the boundary terms at these poles for
simple models, which so far have not been discussed in detail. The main result
is that those boundary terms (for the "un-evolved" observables) arise after
running the Langevin process for a finite time and vanish again as the Langevin
time goes to infinity. This is in contrast to the boundary terms at infinity,
which can be found to occur in the long time limit (cf. the contribution by
D\'enes Sexty).
