We have used long-term AAVSO visual observations and Fourier and wavelet analysis to study the long-term amplitude variations in 29 single-mode and 30 double-mode semiregular (SR) pulsating red giants, in the "long secondary periods" (LSPs) of 26 SR stars, and in 10 Mira stars. The amplitudes of the single-mode SR stars vary by factors of 2 to over 10, on time scales of 18 to 170 (median 44) pulsation periods. The amplitudes of the individual modes in double-mode SR stars behave similarly; the median time scale is 31 pulsation periods, with half lying between 24 and 42. The amplitudes of the two modes seem to vary independently, rather than varying in phase or anti-phase. The amplitudes of the Mira stars vary by typically factors of 1.1 to 1.3, on time scales of about 35 pulsation periods. The amplitudes of the LSPs, in most stars, vary by up to a factor of 2, on time scales of about 30 LSPs or greater. In view of the uncertainty in determining the time scales, we conclude that the time scales of the amplitude variability are similar in each of these four samples. These results should assist theorists in understanding the nature and cause of the amplitudes and their variations.
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