  Let $a(\lambda)$ and $b(\lambda)$ be two polynomials with coefficients in
complex numbers and let $f_{\lamb$ be a one-parameter family of polynomials
indexed by all complex numbers $\lambda$. We study whether there exist
infinitely many complex numbers $\lambda$ such that both $a(\lambda)$ and
$b(\lambda)$ are preperiodic for $f_{\lambda}$.
