The propagation of analyticity for solutions u of
P
(
x
,
D
)
u
=
f
P(x,D)u = f
is studied, in terms of wave front sets, for a large class of differential operators
P
=
P
(
x
,
D
)
P = P(x,D)
of principal type. In view of a theorem by L. Hörmander [9], the results obtained imply rather precise results about the surjectivity of the mapping
P
:
C
∞
(
Ω
)
→
C
∞
(
Ω
)
P:{C^\infty }(\Omega ) \to {C^\infty }(\Omega )
.