General principles of symmetry and conservation are used to construct the hydrodynamic equations for orientationally ordered suspensions of self-propelled particles (SPPs). Without knowledge of the microscopic origins of the ordering or the mechanisms of self-propulsion, we are able to make a number of striking, testable predictions for the properties of these nonequilibrium phases of matter. These include: novel wavelike excitations in vectorially ordered suspensions; the absolute instability of nematic SPP suspensions at long wavelengths; the convective instability of low-Reynolds-number vector-ordered suspensions; and giant number fluctuations in vector-ordered SPP suspensions. (C) 2002 Published by Elsevier Science B.V.