  Let $S$ be a semitopological semigroup. The $wap-$ compactification of
semigroup S, is a compact semitopological semigroup with certain universal
properties relative to the original semigroup, and the $Lmc-$ compactification
of semigroup $S$ is a universal semigroup compactification of $S$, which are
denoted by $S^{wap}$ and $S^{Lmc}$ respectively. In this paper, an internal
construction of the $wap-$compactification of a semitopological semigroup is
constructed as a space of $z-$filters. Also we obtain the cardinality of
$S^{wap}$ and show that if $S^{wap}$ is the one point compactification then
$(S^{Lmc}-S)*S^{Lmc}$ is dense in $S^{Lmc}-S$.
