In this paper, 
we introduce the notion of an almost nonexpansive
curve over a noncommutative semigroup. 
For any almost nonexpansive curve $u$ 
and invariant mean $\mu$, 
we consider generalized fixed point sets  
$F(u)$ and $F_{\mu} (u)$.
Further, we study the asymptotic behavior
of  an almost nonexpansive curve 
over a right reversible semitopological semigroup.