It has been suggested that relativistic outflows may power the jets of active galactic nuclei and gamma-ray bursts. We address the important issue how the kinetic energy of collimated outflows is converted into radiation. It is shown that swept-up ambient matter is quickly isotropized in the outflow region by a relativistic two-stream instability, which provides relativistic particles in the jet without invoking any acceleration process. The fate of the outflow and the spectral evolution of the photon and neutrino emission of the energetic particles is therefore solely determined by the initial condition. ©2001 American Institute of Physics.