Ricardo Weder The $W_{k,p}$-Continuity of the Schroedinger Wave Operators on the Line (40K, LaTex) ABSTRACT. We prove that the wave operators for the Schroedinger equation on the line are continuous on the Sobolev spaces $W_{k,p}, 1 < p < \infty$. Moreover, if the potential is exceptional and $a:= lim_{x \rightarrow - \infty} f_1(x,0)=1$,where $f_1(x,0)$ is a Jost solution at zero energy, the wave operators are continuous on $W_{k,1}$ and in $W_{k,\infty}$.