in this talk we first review the critical threshold phenomena for euler-poisson equations, which arise in the semiclassical approximation of schrodinger-poisson equations and plasma dynamics. we then present a phased space-based level set method for the computation of multi-valued velocity and electric fields of one-dimensional euler-poisson equations. this method uses an implicit eulerian formulation in an extended space, which incorporates both velocity and electric fields into the configuration space. multi-valued velocity and electric fields are captured through common zeros of two level set functions, which solve a linear homogeneous transport equation in the field space. the superposition principle for multi-valued solutions is established.