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In this paper we are interested in symmetries of alternating knots, more precisely in those related to achirality. We call the following statement Tait’s Conjecture on alternating $-$achiral knots: Let $K$ be a prime alternating $-$achiral knot. Then there exists a minimal projection $\Pi$ of $K$ in $S^2\subset S^3$ and an involution $\varphi :S^3\to S^3$ such that: 1) $\varphi$ reverses the orientation of $S^3$; 2) $\varphi \left(S^2\right)=S^2$; 3) $\varphi \left(\Pi \right)=\Pi$; 4) $\varphi$ has two fixed points on $\Pi$ and hence reverses...