In this paper it is proved that for an arbitrary infinitely divisible process $\xi (t)$ and any non-negative infinitely divisible process $\eta (t)$ the distribution of their superposition $\xi (t) = \xi [\eta (t)]$ is also infinitely divisible. The corresponding spectral function $H(x)$ of that process (Levy function) is constructed. The second result is as follows: If in the sum $\zeta (t) = \xi _1 + \cdots + \xi _{\eta (t)} $ all random variables are independent, process $\eta (t)$ has an infinitely divisible distribution, and the random variable $\xi _i $ satisfies condition (V), then the distribution $\zeta (t)$ is infinitely divisible.