  The aim of this paper is to discuss the simpleness of zeros of Stokes
multipliers associated with the differential equation $-\Phi''(X) + W(X)\Phi(X)
=0$, where $ W(X) = X^{m} +a_{1}X^{m-1}+... +a_{m}$ is a real monic polynomial.
We show that, under a suitable hypothesis on the coefficients $a_k$, all the
zeros of the Stokes multipliers are simple.
