  Max Noether's Theorem asserts that if $\ww$ is the dualizing sheaf of a
nonsingular nonhyperelliptic projective curve then the natural morphisms
$\text{Sym}^nH^0(\omega)\to H^0(\omega^n)$ are surjective for all $n\geq 1$.
This is true for Gorenstein nonhyperelliptic curves as well. We prove this
remains true for nearly Gorenstein curves and for all integral nonhyperelliptic
curves whose non-Gorenstein points are unibranch. The results are independent
and have different proofs. The first one is extrinsic, the second intrinsic.
