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Properties of GaAs and InP magnetically tunable far‐infrared (FIR) detectors based on transitions between 1s‐2p(+/0/-) shallow donor states, were studied in magnetic fields up to 8 T. Repeatable low background radiation conditions were obtained by using cyclotron emission from InSb and GaAs as a FIR source. Signal and noise dependence on the temperature, electric, and magnetic fields was investigated. Physical mechanisms responsible for the signal and noise dependencies on the temperature, electric, and magnetic fields are discussed. Local generation‐recombination instabilities are proposed as a physical mechanism causing appearance of the low frequency noise in high magnetic fields.