  Let $(X,d)$ be a metric space and $f: X \rightarrow X$ be a homeomorphism. We
say that a dynamical system $(X,f)$ is \emph{expansive}, with constant of
expansivity $c \in \mathbb{R{^+}}$, if for all $x,y \in X$ , $x \neq y$, exists
$n \in \mathbb{Z}$, such that $d(f^n(x), f^n(y)) >c$. In this paper we will use
the theory of Nonstandard Analysis to study a subfamily of these dynamics,
which verify that for all $x,y \in X$, if $x\neq y$ then the set $\lbrace n \in
\mathbb{Z} : d(f^n(x), f^n(y) > c \rbrace$ is infinite.
