  We prove new results on projective normality, normal presentation and higher
syzygies for a surface of general type $X$ embedded by adjoint line bundles
$L_r = K + rB$, where $B$ is a base point free, ample line bundle. Our main
results determine the $r$ for which $L_r$ has $N_p$ property. In corollaries,
we will relate the bounds on $r$ to the regularity of $B$. Examples in the last
section show that several results are optimal.
