  Let X be a complex analytic manifold and D \subset X a free divisor.
Integrable logarithmic connections along D can be seen as locally free {\cal
O}_X-modules endowed with a (left) module structure over the ring of
logarithmic differential operators {\cal D}_X(\log D). In this paper we study
two related results: the relationship between the duals of any integrable
logarithmic connection over the base rings {\cal D}_X and {\cal D}_X(\log D),
and a differential criterion for the logarithmic comparison theorem. We also
generalize a formula of Esnault-Viehweg in the normal crossing case for the
Verdier dual of a logarithmic de Rham complex.
