In this talk, we study the local structure of singularities of the nodal set of segregated configurations associated with two classes of singularly perturbed elliptic systems. These systems arise in Bose–Einstein condensates and in competing models in population dynamics. We prove the uniqueness and the continuous dependence of the blowups at singular points of given homogeneity. As a consequence we obtain the rectifiability as well as local structures of singularities.