  Given closed topological $n$-manifold $M^n$, $n\geq 2$, one introduces the
classes of Smale regular $SRH(M^n)$ and Smale semi-regular $SsRH(M^n)$
homeomorphisms of $M^n$ with $SRH(M^n)\subset~SsRH(M^n)$. The class $SRH(M^n)$
contains all Morse-Smale diffeomorphisms, while $SsRH(M^n)$ contains
A-diffeomorphisms with trivial and some nontrivial basic sets provided $M^n$
admits a smooth structure. We select invariant sets that determine dynamics of
Smale homeomorphisms. This allows us to get necessary and sufficient conditions
of conjugacy for $SRH(M^n)$ and $SsRH(M^n)$. We deduce applications for some
Morse-Smale diffeomorphisms and A-diffeomorphisms with codimension one
expanding attractors.
