A search for the direct production of charginos and neutralinos in final states with at least two hadronically decaying tau leptons is presented. The analysis uses a dataset of $pp$ collisions corresponding to an integrated luminosity of 36.1 fb$^{-1}$, recorded with the ATLAS detector at the Large Hadron Collider at a centre-of-mass energy of $\sqrt{s}=$ 13 TeV. No significant deviation from the Standard Model background expectation is observed. Limits are derived in scenarios of $\tilde{\chi}_{1}^{+}\tilde{\chi}_{1}^{-}$ pair production and of $\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{2}^{0}$ and $\tilde{\chi}_{1}^{+}\tilde{\chi}_{1}^{-}$ production. Chargino masses up to 630 GeV are excluded at 95\% confidence level in the scenario of direct production of $\tilde{\chi}_{1}^{+}\tilde{\chi}_{1}^{-}$ for a massless $\tilde{\chi}_{1}^{0}$. Common $\tilde{\chi}_{1}^{\pm}$, $\tilde{\chi}_{2}^{0}$ masses up to 760 GeV are excluded in the case of production of $\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{2}^{0}$ and $\tilde{\chi}_{1}^{+}\tilde{\chi}_{1}^{-}$ assuming a massless
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