  The phase diagram of the two-leg Kondo ladder is investigated using
computational techniques. Ferromagnetism is present, but only at small
conduction electron densities and robust Kondo coupling $J$. For densities
$n\gtrsim0.4$ and any Kondo coupling, a paramagnetic phase is found. We also
observed spin dimerization at densities $n$=1/4 and $n$=1/2. The spin structure
factor at small $J$ peaks at $\vec{q}$=$(2n,0)\pi$ for $n\lesssim0.5$, and at
$\vec{q}$=$(n,1)\pi$ for $n\gtrsim0.5$. The charge structure factor suggests
that electrons behave as free particles with spin-1/2 (spin-0) for small
(large) $J$.
