In this paper we study exceptional Dehn fillings on hyperbolic knot manifolds which contain an essential once-punctured torus. Let
M
M
be such a knot manifold and let
β
\beta
be the boundary slope of such an essential once-punctured torus. We prove that if Dehn filling
M
M
with slope
α
\alpha
produces a Seifert fibred manifold, then
Δ
(
α
,
β
)
≤
5
\Delta (\alpha ,\beta )\leq 5
. Furthermore we classify the triples
(
M
;
α
,
β
)
(M; \alpha ,\beta )
when
Δ
(
α
,
β
)
≥
4
\Delta (\alpha ,\beta )\geq 4
. More precisely, when
Δ
(
α
,
β
)
=
5
\Delta (\alpha ,\beta )=5
, then
M
M
is the (unique) manifold
W
h
(
−
3
/
2
)
Wh(-3/2)
obtained by Dehn filling one boundary component of the Whitehead link exterior with slope
−
3
/
2
-3/2
, and
(
α
,
β
)
(\alpha , \beta )
is the pair of slopes
(
−
5
,
0
)
(-5, 0)
. Further,
Δ
(
α
,
β
)
=
4
\Delta (\alpha ,\beta )=4
if and only if
(
M
;
α
,
β
)
(M; \alpha ,\beta )
is the triple
(
W
h
(
−
2
n
±
1
n
)
;
−
4
,
0
)
\displaystyle (Wh(\frac {-2n\pm 1}{n}); -4, 0)
for some integer
n
n
with
|
n
|
>
1
|n|>1
. Combining this with known results, we classify all hyperbolic knot manifolds
M
M
and pairs of slopes
(
β
,
γ
)
(\beta , \gamma )
on
∂
M
\partial M
where
β
\beta
is the boundary slope of an essential once-punctured torus in
M
M
and
γ
\gamma
is an exceptional filling slope of distance
4
4
or more from
β
\beta
. Refined results in the special case of hyperbolic genus one knot exteriors in
S
3
S^3
are also given.