Moduli spaces of quadratic differentials with prescribed singularities are
not necessarily connected. We describe here all cases when they have a special
hyperelliptic connected component. We announce the general classification
theorem: up to the four exceptional cases in low genera the strata of
meromorphic quadratic differentials are either connected, or have exactly two
connected components, and one of the two components is hyperelliptic.Comment: references added. 23 pages, 5 figure