Let $mathcal{K}^{prime}_M$ be the generalized tempered distributions of $e^{M(t)}$-growth, where the function M(t) grows faster than any linear functions as ${mid}t{mid}{ ightarrow}{infty}$, and let $K^{prime}_M$ be the Fourier transform spaces of $mathcal{K}^{prime}_M$. We obtain the relationship between certain classes of analytic functions in tubes, $mathcal{K}^{prime}_M$ and $K^{prime}_M$.