  We show that log flat torsors over a family $X/S$ of nodal curves under a
finite flat commutative group scheme $G/S$ are classified by maps from the
Cartier dual of $G$ to the log Jacobian of $X$. We deduce that fppf torsors on
the smooth fibres of $X/S$ can be extended to global log flat torsors under
some regularity hypotheses.
