  In two fundamental classical papers, Masur and Veech have independently
proved that the Teichmueller geodesic flow acts ergodically on each connected
component of each stratum of the moduli space of quadratic differentials. It is
therefore interesting to have a classification of the ergodic components. Veech
has proved that these strata are not necessarily connected. In a recent work,
Kontsevich and Zorich have completely classified the components in the
particular case where the quadratic differentials are given by the global
square of Abelian differentials.
  Here we are interested in the complementary case. In a previous paper, we
have described some particular component, namely the hyperelliptic connected
components, and showed that some strata are non-connected. In this paper, we
give the general classification theorem: up to four exceptional cases in low
genera, the strata of meromorphic quadratic differentials are either connected,
or have exactly two connected components. In this last case, one component is
hyperelliptic, the other not.
  Our proof is based on a new approach of the so-called Jenkins-Strebel
differential. We will present and use the notion of generalized permutations.
