  We study the production at future $e^+e^-$ linear colliders of the heavy
neutral Higgs bosons $H$ and $A$ of the minimal supersymmetric standard model
in association with top and bottom quarks. The cross sections have a strong
dependence on the parameter $\tan\beta$, and thus provide a good way to
determine it. At a linear collider with $\sqrt s = 0.5-1$ TeV and expected
integrated luminosities, we find significant sensitivities for determining
$\tan\beta$. In the Supergravity scenario, the sensitivity is particularly
strong for $\tan\beta > 10$, reaching a 15% or better measurement. In the
general MSSM scenario, the interplay between the $4b$ and $4t$ channels results
in a good determination for $\tan\beta < 10$, while the sensitivity is weakened
for higher values of $\tan\beta$.
