  Let $\k$ be an arbitrary field. For any fixed badly approximable power series
$\Theta$ in $\k((X^{-1}))$, we give an explicit construction of continuum many
badly approximable power series $\Phi$ for which the pair $(\Theta, \Phi)$
satisfies the Littlewood conjecture. We further discuss the Littlewood
conjecture for pairs of algebraic power series.
