  Let $X$ be a compact metric space and $\Phi=\{\varphi_t\}_{t\in\mathbb{R}}$
be a continuous flow on $X$. We introduce two types of topological pressure for
family of discontinuous potentials $a=\{a_t\}_{t>0}$. First, define the
topological pressure of family of measurable potentials $a=\{a_t\}_{t>0}$ on a
subset $Z$ for flow and proof its invariant principle. The second topological
pressure is defined on a invariant subset having a nested family of subsets, we
also proof its invariant principle.
