Nested classes of C-semi-selfdecomposable distributions

We get a representation of Lévy measures of (C,m)-semi-selfdecomposable distributions, which extend c-semi-selfdecomposable distributions of Maejima and Naito (1998). We prove that for every pair (C,m) there exists a distribution which is exactly (C,m)-semi-selfdecomposable. Explicit examples are given.