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 .