Singular bielliptic curves and Weierstrass points

Here we study the Weierstrass points of singular bielliptic curves in characteristic 0. Most of our results are existence results of the type "there exists a bielliptic curve Y with certain singular points and with a weierstrass point P ∈ Y_{reg} with a prescribed gap sequence". Another main result is a smoothness one for the set of all genus g bielliptic curves with prescribed singularities.