  Let $X$ be a smooth geometrically connected projective curve over the field
of fractions of a discrete valuation ring $R$, and $\mathfrak{m}$ a modulus on
$X$, given by a closed subscheme of $X$ which is geometrically reduced. The
generalized Jacobian $J_\mathfrak{m}$ of $X$ with respect to $\mathfrak{m}$ is
then an extension of the Jacobian of $X$ by a torus. We describe its N\'eron
model, together with the character and component groups of the special fibre,
in terms of a regular model of $X$ over $R$. This generalizes Raynaud's
well-known description for the usual Jacobian. We also give some computations
for generalized Jacobians of modular curves $X_0(N)$ with moduli supported on
the cusps.
