The anomalous Doppler instability is investigated for two‐dimensional velocity distributionsf(v∥,v⊥) appropriate for lower‐hybrid current drive. In this case, in contrast to the runaway electron problem, this mode becomes unstable athighdensitywhen the ratio &ohgr;2pe/ &ohgr;2ceis sufficiently large. Increasing the maximum velocityv2of the rf (radio‐frequency) plateau,v1≤v∥≤v2, is also a destabilizing influence. In this paper expressions are given for the growth rate of the electrostatic waves obeying the dispersion relation &ohgr;=&ohgr;pe(1+&ohgr;2pe/ &ohgr;2ce)−1/2k∥/k, employing both analytic expressions forf(v∥,v⊥) and numerical solutions forffrom the two‐dimensional Fokker–Planck equation. The analytical and numerical results are in close agreement.