This paper deals with the chaotic behavior of linear operators on Banach spaces in both discrete and continuous cases. The inheritances of chaos for linear operators and
C
0
C_0
-semigroups are obtained. More precisely, for any positive integer
n
≥
2
n\geq 2
, both Li-Yorke
n
n
-chaos and distributional
n
n
-chaos are proved to be inherited under iterations for a linear operator. One further shows that a
C
0
C_0
-semigroup
{
T
t
}
t
≥
0
\{T_t\}_{t\geq 0}
and every single operator
T
t
T_t
share the same Li-Yorke
n
n
-scrambled set and distributionally
n
n
-scrambled set for any positive integer
n
≥
2
n\geq 2
. In particular, the Li-Yorke
n
n
-chaos and distributional
n
n
-chaos become the Li-Yorke chaos and distributional chaos when
n
=
2
n=2
, respectively. Some equivalent criteria for dense
n
n
-chaos and generic
n
n
-chaos of linear operators and
C
0
C_0
-semigroups are also established for any
n
≥
2
n\geq 2
.