  We consider flows $(X,T)$, given by actions $(t, x) \to tx$, on a compact
metric space $X$ with a discrete $T$ as an acting group. We study a new class
of flows - the \textsc{Strongly Rigid} ($ \mathbf {SR} $) \ flows, that are
properly contained in the class of distal ($ \mathbf D $) flows and properly
contain the class of all equicontinuous ($ \mathbf {EQ} $) flows. Thus,
$\mathbf {EQ} \ \text{flows} \subsetneqq \mathbf {SR} \ \text{flows}
\subsetneqq \mathbf{ D} \ \text{flows}$.
  The concepts of equicontinuity, strong rigidity and distality coincide for
the induced flow $(2^X,T)$. We observe that strongly rigid $(X,T)$ gives
distinct properties for the induced flow $(2^X,T)$ and its enveloping semigroup
$E(2^X)$. We further study strong rigidity in case of particular semiflows
$(X,S)$, with $S$ being a discrete acting semigroup.
