  We prove that the categories of Gelfand-Zeitlin modules of
$\mathfrak{g}=\mathfrak{gl}_n$ and Whittaker modules associated with a
semi-simple complex finite-dimensional algebra $\mathfrak{g}$ are extension
full in the category of all $\mathfrak{g}$-modules. This is used to estimate
and in some cases determine the global dimension of blocks of the categories of
Gelfand-Zeitlin and Whittaker modules.
