Abstract: Hensel minimality is a class of conditions introduced as valued field analogue(s) (in characteristic 0) of o-minimality. We explore groups definable in 1-h-minimal fields (the second weakest of the Hensel-minimality conditions), extending the analogy with o-minimality. We prove that infinite such groups admit a unique definable (weak) manifold structure with respect to which they are strictly differential. We further show that germs of definable local subgroups are determined by their Lie subalgebras. On the way we develop the basic theory of definable morphisms between definable manifolds.