We consider k-equivariant Schroedinger maps in two space dimensions, with values into the unit sphere. It has been known for some time that for $k=1$, near soliton  solutions can blow up in finite time, while for  k > 2 such solutions are global and scatter at infinity. The aim of this talk will be to describe some recent results in the intermediate case k=2, in joint work with Ioan Bejenaru and Mohandas Pillai.