Experimental results are presented for the heating of a 4 m long plasma confined by a uniform magnetic field of 4–5 kG by an intense relativistic electron beam. Beam parameters were 0.5–1 MeV, 25–80 kA, 60–70 nsec pulse duration, and electron density of 2–5×1011/cm3. The initial plasma density ranged from 5×1013/cm3to 4×1015/cm3and the electron temperature was 1–3 eV. The lower density cases were partially ionized withTe≫Ti, and the higher density cases were highly ionized withTe≈Ti. In all cases, the energy coupled from the beam to the plasma was greater than can be explained by binary collisions between beam electrons and the plasma particles. Beam energy transferred to the plasma ranged from 2–7%/m, and was uniform over the 4 m length of the plasma. Over most of the density range tested, 5×1013/cm3to 1.5×1015/cm3, the plasma heating cannot be explained by classical processes. These results are found to be explained quantitatively by the use of a full nonlinear treatment of the electron‐electron two‐stream instability in the kinetic regime.