  By studying $\pi\pi$ scattering amplitudes in the large $N_c$ limit, we
clarify the $N_c$ dependence of the $S$ matrix pole position. It is
demonstrated that analyticity and the $N_c$ counting rule exclude the existence
of $S$ matrix poles with ${\cal M}, \Gamma\sim O(1)$. Especially the properties
of $\sigma$ and $f_0(980)$ with respect to the $1/N_c$ expansion are discussed.
We point out that in general tetra-quark resonances do not exist.
