This paper deals with determination of the critical modulation frequency (CMF) for random amplitude and frequency changes in a sinusoidal signal. The CMF is defined as the smallest modulation frequency for which AM and FM detection thresholds, expressed as modulation indices, reach the same values. The random amplitude and frequency changes were produced by modulators which were sinusoidal waves with randomly changing amplitude from period to period. The results indicate that the CMF is an increasing function of the carrier frequency and the sound pressure level. It is also shown that thresholds for detecting modulation, when expressed as root-meansquare modulation index, do not depend on the character of the modulating signal, i.e. whether this signal is periodic or random. Further, the CMF is independent of the character of the modulating signal.