  Let $(X,J,g,\omega)$ be a compact $2n$-dimensional almost-K\"ahler manifold.
We prove primitive decompositions of $\partial$-,
$\overline{\partial}$-harmonic forms on $X$ in bidegree $(1,1)$ and $(n-1,n-1)$
(such bidegrees appear to be optimal). We provide examples showing that in
bidegree $(1,1)$ the $\partial$- and $\overline{\partial}$-decompositions
differ.
