Does merger and acquisition (M&A) activity occur in waves, that is, are there oscillations between low and high levels of M&A activity? The answer to this question is important in developing univariate as well as structural models of explaining and forecasting the stochastic behavior of M&A activity. There is evidence to suggest that aggregate U.S. time-series data on merger and acquisition (M&A) activity exhibit a "wave" behavior, which has been modeled by fitting either a two-state Markov switching-regime model or a sine-wave model to the data. This study provides an alternative characterization of the temporal patterns in M&A as a nonlinear process with strongly persistent or long-memory dynamics. The apparent level changes or partial cycles of differing magnitudes in aggregate M&A time series are consistent with an underlying data generating process exhibiting long memory. Time- and frequency-domain estimation methods are applied to a long M&A time series constructed by Town (1992), covering approximately a century of merger activity in the U.S. economy. We find significant evidence of long-term cyclical behavior, nonperiodic in nature, in the M&A time series, even after accounting for potential shifts in the mean level of the series. A shock to M&A activity exhibits significant persistence as it is damped at the very slow hyperbolic rate, but it eventually dissipates. We provide both theoretical and empirical rationales for the presence of fractional dynamics with long-memory features in M&A activity. Theoretically, long-term dependence may be due to persistent differences in firm valuation between stockholders and nonstockholders following an "economic disturbance," as suggested by Gort (1969). Empirically, long-memory dynamics in M&A activity may reflect the statistical properties of fundamental factors underlying its behavior, as several of the proposed determinants of M&A activity have been shown to exhibit strong persistence.