  Dans cette note on decrit le champ des courbes hyperelliptiques lisses
defines sur un corps algebriquement clos de caracteristique deux comme un champ
quotient. On en deduit le groupe de Picard.
  -----
  In this note we describe the stack ${\cal H}_g$ of smooth hyperelliptic
curves of genus $g$ over an algebraically closed field of characteristic two,
as a quotient stack of a smooth variety of dimension $3g+5$ by a non reductive
algebraic group, extending a well known result of Vistoli. As an application,
we show the Mumford-Vistoli description of the Picard group of the stack ${\cal
H}_g$ is valid in this characteristic. We also describe the natural
stratification of ${\cal H}_g$ by means of higher ramification data. We point
out that after stable compactification $\bar {\cal H}_g$ is not smooth in
codimension at least two.
