Let ${\mathcal F}_I=\{f:I \to I| f(x)= (Ax+B)/(Cx+D); AD-BC \neq 0 \}$, where
$I$ is an interval. For $x\in I$, let ${\Omega}_x$ be the orbit of $x$ under
the action of the semigroup of functions generated by $f,g \in {\mathcal F}_I$.
Our main result in this paper is to describe all $f,g \in {\mathcal F}_I$ such
that $\Omega_x$ is dense in $I$ for all $x$.