  The radical $J(V)$ of a vertex operator algebra $V$ is defined to be the
subspace of $V$ consisting of vectors $v$ such that the zero mode $o(v)=0$ on
$V$ where $o(v)=v_{wt v-1}$ if $v$ is homogeneous. We establish various facts
about $o(v),$ including the determination of $J(V)$ which is shown to be
essentially equal to $(L(0)+L(-1))V.$
