  The Laplace-Beltrami operator on cusp manifolds has continuous spectrum. The
resonances are complex numbers that replace the discrete spectrum of the
compact case. They are the poles of a meromorphic function $\varphi(s)$, $s\in
\mathbb{C}$, the \emph{scattering determinant}. We construct a semi-classical
parametrix for this function in a half plane of $\mathbb{C}$ when the curvature
of the manifold is negative. We deduce that for manifolds with one cusp, there
is a zone without resonances at high frequency. This is true more generally for
manifolds with several cusps and generic metrics.
  We also study some exceptional examples with almost explicit sequences of
resonances away from the spectrum.
