  Three searches for the direct production of staus or charginos and
neutralinos in final states with at least two hadronically decaying
$\tau$-leptons are presented. For chargino and neutralino production, decays
via intermediate staus or $W$ and $h$ bosons are considered. The analysis uses
a dataset of $pp$ collisions corresponding to an integrated luminosity of 139
$fb^{-1}$, recorded with the ATLAS detector at the Large Hadron Collider at a
centre-of-mass energy of 13 TeV. No significant deviation from the expected
Standard Model background is observed and SUSY particle mass limits at 95%
confidence level are obtained in simplified models. For direct production of
$\tilde~{\chi}^{+}_{1}\tilde~{\chi}^{-}_{1}$, chargino masses are excluded up
to 970 GeV, while $\tilde~{\chi}^{\pm}_1$ and $\tilde~{\chi}^0_2$ masses up to
1160 GeV (330 GeV) are excluded for
$\tilde~{\chi}^{\pm}_1\tilde~{\chi}^0_2$/$\tilde~{\chi}^+_1\tilde~{\chi}^-_1$
production with subsequent decays via staus ($W$ and $h$ bosons). Stau masses
up to 500 GeV are excluded for mass degenerate $\tilde~{\tau}_{L,R}$ scenarios
and up to 425 GeV for $\tilde~{\tau}_L$-only scenarios. Sensitivity to
$\tilde~{\tau}_R$-only scenarios from the ATLAS experiment is presented here
for the first time, with $\tilde~{\tau}_R$ masses excluded up to 350 GeV.
