We derive semiclassical neutrino-electron transport equations in the collisionless (Vlasov) limit from the coupled Dirac equations, incorporating the charged and neutral weak current-current as well as electromagnetic interactions. A corresponding linear response theory is derived. In particular, we calculate the response functions for a variety of beam-plasma geometries, which are of interest in a supernova scenario. We apply this to the study of plasmons and to a new class of collective pharon resonance modes, which are characterized by $\ensuremath{\omega}<q.$ We find that the growth rates of the unstable modes correspond to a strongly temperature $(\ensuremath{\propto}{T}_{\ensuremath{\nu}}^{2}{T}_{e}^{3})$ and linearly momentum dependent e-folding length of about ${10}^{10} \mathrm{km}$ under typical conditions for type II supernovas. This appears to rule out such long-wavelength collective modes as an efficient means of depositing neutrino energy into the plasma sphere.