  Let $x\geqslant 3$. For $1\leqslant n\leqslant x$ an integer, let $\omega(n)$
be its number of distinct prime factors. We show that $\omega(n-1)$ satisfies
an Erd\H{o}s-Kac type theorem whenever $\omega(n)=k$ where $1\leqslant
k\ll\log\log x$, thus extending a result of Halberstam.
