  In this paper we study the projective normality of certain Artin-Schreier
curves $Y_f$ defined over a field $\F$ of characteristic $p$ by the equations
$y^q+y=f(x)$, $q$ being a power of $p$ and $f\in \F[x]$ being a polynomial in
$x$ of degree $m$, with $(m,p)=1$. Many $Y_f$ curves are singular and so, to be
precise, here we study the projective normality of appropriate projective
models of their normalizations.
