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The response of an automatic gain control (AGC) amplifier to two narrow-band input signals is analyzed with respect to weak signal suppression and cross-product generation. A linear control characteristic is assumed. Results are obtained for a wide range of relative input-signal levels and frequency spacings. It is shown that the weak signal suppression and cross-product generation decrease, with increasing frequency separation, relative to the closed-loop AGC bandwidth. With the proper choice of AGC time constant and frequency spacing, it is possible to control the total power level of several signals without undesirable interaction among the signals. For certain asymptotic results, it is shown that the AGC performance coincides with that of a hard-limiter.