1. Let the polynomial $x^{3}-x-a$ and the polynomial $x^{2}+x$ $-a$ have a non-constant common factor, then $a=$ $\qquad$ .
II. 1.0 or 6.
Since $\left(x^{3}-x-a\right)-\left(x^{2}+x-a\right)=x(x+1)(x-2)$, the common factor of $x^{3}-x-a$ and $x^{2}+x-a$ must be one of $x$, $x+1$, or $x-2$.
When the common factor is $x$ or $x+1$, $a=0$;
When the common factor is $x-2$, $a=6$.

Therefore, $a=0$ or 6.