  We construct the hydrodynamic equations for {\em suspensions} of
self-propelled particles (SPPs) with spontaneous orientational order, and make
a number of striking, testable predictions:(i) SPP suspensions with the
symmetry of a true {\em nematic} are {\em always} absolutely unstable at long
wavelengths.(ii) SPP suspensions with {\em polar}, i.e., head-tail {\em
asymmetric}, order support novel propagating modes at long wavelengths,
coupling orientation, flow, and concentration. (iii) In a wavenumber regime
accessible only in low Reynolds number systems such as bacteria, polar-ordered
suspensions are invariably convectively unstable.(iv) The variance in the
number N of particles, divided by the mean <N>, diverges as $<N >^{2/3}$ in
polar-ordered SPP suspensions.
