  We analyze the Moyal star product in deformation quantization from the
resurgence theory perspective. By putting algebraic conditions on Borel
transforms, one can define the space of ``algebro-resurgent series'' (a
subspace of $1$-Gevrey formal series in $i\hbar/2$ with coefficients in
$C\{q,p\}$), which we show is stable under Moyal star product.
