  We study resonances for the generator of a diffusion with small noise in
$R^d$ :$ L_\epsilon = -\epsilon\Delta + \nabla F \cdot \nabla$, when the
potential F grows slowly at infinity (typically as a square root of the norm).
The case when F grows fast is well known, and under suitable conditions one can
show that there exists a family of exponentially small eigenvalues, related to
the wells of F . We show that, for an F with a slow growth, the spectrum is R+,
but we can find a family of resonances whose real parts behave as the
eigenvalues of the "quick growth" case, and whose imaginary parts are small.
