Let
T
=
(
T
1
,
T
2
,
.
.
.
,
T
n
)
\mathbf { T} = (T_{1},T_{2},...,T_{n})
be a doubly commuting
n
n
-tuple of
p
p
-hyponormal operators
T
j
T_{j}
with unitary operators
U
j
U_{j}
from the polar decompositions
T
j
=
U
j
|
T
j
|
(
j
=
1
,
.
.
.
,
n
)
T_{j} = U_{j}|T_{j}| (j=1,...,n)
. Let
U
=
(
U
1
,
.
.
.
,
U
n
)
\mathbf { U} = (U_{1},...,U_{n})
and
A
=
|
T
1
|
⋯
|
T
n
|
A = |T_{1}| \cdots |T_{n}|
. In this paper, we will show relations between the Taylor spectrum
σ
T
(
T
)
\sigma _{T}(\mathbf { T})
and the Xia spectrum
σ
X
(
U
,
A
)
\sigma _{X}(\mathbf { U},A)
.