ESPAR (Electronically Steerable Passive Array Radiator) antennas were proposed as candidates for low-cost analog adaptive beamforming. The radiation pattern is controlled in an azimuthal plane by variable reactors loaded on each passive element. This paper estimates the frequency bandwidth of an ESPAR antenna in a single beam scanning operation. Bandwidth in terms of gain is predicted statistically as functions of beam direction and dynamic range of variable reactance. The -3 dB bandwidth of 7-element ESPAR antennas can be about 30%, 25% and 15% for the range of reactance of -100Ω Xn 100Ω, -50Ω Xn 50Ω and -100Ω Xn 0Ω, respectively, while the improper choice of reactance sets results in narrow bandwidth less than 5%.