  We study the problem of constructing a contragredient functor on the category
of admissible locally analytic representations of a p-adic analytic group G. A
naive contragredient does not exist. As a best approximation, we construct an
involutive "duality" functor from the bounded derived category of modules over
the distribution algebra of G with coadmissible cohomology to itself. On the
subcategory corresponding to complexes of smooth representations, this functor
induces the usual smooth contragredient (with a degree shift). Although we
construct our functor in general we obtain its involutivity, for technical
reasons, only in the case of locally Qp-analytic groups.
