  We prove the following form of the Clemens conjecture in low degree. Let
$d\le9$, and let $F$ be a general quintic threefold in $\IP^4$. Then (1)~the
Hilbert scheme of rational, smooth and irreducible curves of degree $d$ on $F$
is finite, nonempty, and reduced; moreover, each curve is embedded in $F$ with
normal bundle $\O(-1)\oplus\O(-1)$, and in $\IP^4$ with maximal rank. (2)~On
$F$, there are no rational, singular, reduced and irreducible curves of degree
$d$, except for the 17,601,000 six-nodal plane quintics (found by Vainsencher).
(3)~On $F$, there are no connected, reduced and reducible curves of degree $d$
with rational components.
