Beam-plasma interactions associated with the cross-field injection of electron beams from spacecraft are investigated by means of two-dimensional (three velocity component) electrostatic particle simulations and are compared with those for parallel injection. The degree of spacecraft charging and the nature of the plasma response depends on the ratio of the plasma response time trp to the beam stagnation time ts. In particular, when trp/ts≲0.4 and the spacecraft size is comparable to the return current region, the spacecraft charging is reduced sufficiently so that the beam is able to escape from the near environment of the spacecraft. The parameters which determine the value of the ratio trp/ts are the density of the ambient plasma relative to the beam density, the beam width and energy and the spacecraft size. Thin energetic beams injected from wide spacecraft are most easily able to escape, with the spacecraft potential being proportional to the parallel beam energy rather than to the total energy. Strong space-charge oscillations near the lower hybrid and upper hybrid frequencies are produced as the beam propagates into the plasma. These oscillations tend to cause beams injected across the field lines to lose their coherence after about one or two gyrations. The beam electrons are scattered into a hollow cylinder with radius equal to the beam electron gyroradius and thickness of about two beam Debye lengths. Parallel injected beams experience similar forces which cause the beam to expand to fill a solid cylinder of a comparable thickness. The return currents produced by both cross-field and parallel beam injection have an extent across the field lines of the order of the gyroradius of a plasma ion accelerated up to about the spacecraft potential. ¿ American Geophysical Union 1988