7. Let $x, y$ be real numbers, and satisfy
$$
\left\{\begin{array}{l}
(x-1)^{3}+1997(x-1)=-1, \\
(y-1)^{3}+1997(y-1)=1 .
\end{array} \text { Then } x+y=\right.
$$
$\qquad$
$f(x)=x^{3}+1997 x+1$ is monotonically increasing on $\mathbf{R}$, according to the problem, $f(x-1)=f(1-y)=0$ $\Rightarrow x-1=1-y \Rightarrow x+y=2$