  We establish analyticity of the subcritical and critical quasi-geostrophic
equations in critical Besov spaces. The main method is so-called Gevrey
estimates, which is motivated by the work of Foias and Temam. We show that mild
solutions \theta(t), are Gevrey regular, i.e. they satisfy the estimate
\sup_{t>0}\|e^{\alpha t^{1/\gamma}\Lambda_1}\theta(t)\|_{\cap L}<\infty. for a
suitably chosen \alpha>0 and a scaling invariant Besov space {\cap L}.
