  Let $\Phi^\l$ be an algebraic family of Drinfeld modules defined over a field
$K$ of characteristic $p$, and let $\bfa,\bfb\in K[\l]$. Assume that neither
$\bfa(\l)$ nor $\bfb(\l)$ is a torsion point for $\Phi^\l$ for all $\l$. If
there exist infinitely many $\l\in\Kbar$ such that both $\bfa(\l)$ and
$\bfb(\l)$ are torsion points for $\Phi^\l$, then we show that for each
$\l\in\Kbar$, we have that $\bfa(\l)$ is torsion for $\Phi^\l$ if and only if
$\bfb(\l)$ is torsion for $\Phi^\l$. In the case $\bfa,\bfb\in K$, then we
prove in addition that $\bfa$ and $\bfb$ must be $\Fpbar$-linearly dependent.
