Let
p
t
(
x
)
p_t(x)
,
f
t
(
x
)
f_t(x)
and
q
t
∗
(
x
)
q_t^*(x)
be the densities at time
t
t
of a real Lévy process, its running supremum and the entrance law of the reflected excursions at the infimum. We provide relationships between the asymptotic behaviour of
p
t
(
x
)
p_t(x)
,
f
t
(
x
)
f_t(x)
and
q
t
∗
(
x
)
q_t^*(x)
, when
t
t
is small and
x
x
is large. Then for large
x
x
, these asymptotic behaviours are compared to this of the density of the Lévy measure. We show in particular that, under mild conditions, if
p
t
(
x
)
p_t(x)
is comparable to
t
ν
(
x
)
t\nu (x)
, as
t
→
0
t\rightarrow 0
and
x
→
∞
x\rightarrow \infty
, then so is
f
t
(
x
)
f_t(x)
.