For a locally compact Hausdorff semigroup $S$, 
the $L^\infty$-representation algebra $R(S)$ 
was extensively studied by Dunkl and Ramirez. 
The Fourier- Stieltjes algebra $F(S)$ 
of a topological semigroup was introduced 
and studied by Lau. The aim of this paper 
is to investigate the amenability of these algebras.