Experiments have been made of magnetostatic wave propagation through an axially magnetized, [100]oriented, unpolished YIG rod of circular cross section, at increasing incident power levels, and instability phenomena have been noted. The transmitted power was observed as a function of frequency and the power level was increased until instabilities occurred in the form of oscillations superimposed on the transmission spectrum. The instabilities started first in the cutoff region of the magnetostatic volume modes (j=-yH dc ) and extended towards higher frequencies for increasing incident power. The onset occurred for incident power values of a few tens of mW (a few mW into the crystal). For very high values of incident power (~1 W), strong transmission below -yHdc was also noted. The oscillations were then examined at fixed microwave frequency, both in the time and in the frequency domain and were found to be of the order of the hundreds of kHz, and to be highly unstable, as shown by jitter in the time representation and random noise in the spectral analysis. The instability effects seemed to be rather insensitive to the sample orientation. The results are discussed in the light of existing theories.