Low‐frequency noise measurements have been made throughout the entire useful bias range of germanium and GaAs Esaki diodes. Evidence is presented in agreement with Esaki and Yajima that a near square‐law relationship exists between the mean‐square, short‐circuit noise current and excess current for bias voltages beyond the valley voltage in germanium diodes. Attempts to find a like relationship in GaAs were not conclusive. Measurements of the noise within the negative‐resistance regions of the diodes showed a nearly continuous exponential relationship between excess noise and bias for the germanium units and a similar plot was obtained for the GaAs diodes, except a well‐defined peak in the noise current was found at about 0.2 v forward bias. The evidence that the results indicate a rather continuous distribution of allowed states in the forbidden band of the germanium samples and a possible localized maximum in these states in the GaAs samples is discussed.