  Let (X, O_X) be an algebraic manifold in characteristic 0, or an analytic
manifold over \C. A standard theorem says that a left D_X-module M, which is
coherent as an O_X-module, is locally free. This theorem has a generalization
to the adically complete algebraic setting, in a paper by Ogus from 1973.
  In the present paper we take a new look at the work of Ogus. We provide a
detailed proof of the theorem on D-modules, and extend it to the non-noetherian
setting. We also give another proof of an interesting result of Ogus about
adically complete modules (slightly extended).
  In the Appendix we discuss a related error in a book by Bjork.
