  We study the statistical distributions of the resonance widths ${\cal P}
(\Gamma)$, and of delay times ${\cal P} (\tau)$ in one dimensional
quasi-periodic tight-binding systems with one open channel. Both quantities are
found to decay algebraically as $\Gamma^{-\alpha}$, and $\tau^{-\gamma}$ on
small and large scales respectively. The exponents $\alpha$, and $\gamma$ are
related to the fractal dimension $D_0^E$ of the spectrum of the closed system
as $\alpha=1+D_0^E$ and $\gamma=2-D_0^E$. Our results are verified for the
Harper model at the metal-insulator transition and for Fibonacci lattices.
