The agricultural economics literature, both academic and trade, has discussed the assumed presence of cycles in livestock markets such as cattle and hogs for a very long time. Since Jarvis (1974), there has been considerable discussion over how these cycles impact optimal economic decision making. Subsequent studies such as Rucker, Burt, and LaFrance (1984), Hayes and Schmitz (1987), Foster and Burt (1992), Rosen, Murphy, and Scheinkman (1994), and Hamilton and Kastens (2000) have all investigated some aspect of how biological factors, economic events, or economic actions could be causes of and/or responses to cycles in hog and cattle inventories. There has also been debate, again both in the academic and trade literature, over the length of the cycle(s) present in hog and cattle stocks. To provide both academics and producers with accurate information on the number and periods of cycles that might be present in hog and cattle inventories, this paper provides a purely statistical view of the matter. Using over 140 years of annual data on cattle and hog inventory levels, we estimate Bayesian autoregressive, trend-stationary models on cattle inventories, hog inventories, and the growth rate of cattle inventories. We then use those models to find the posterior distributions of both the number of cycles present in each series and the period lengths of those cycles. We find multiple cycles present in all three series. Cattle inventory results show clear evidence in favor of 4.5, 6, and 11 year cycles with other cycles present but not as clearly identified. Hog inventory results identify five cycles with periods of approximately 4.5, 5.4, 6.8, 10 and 13 years. The data on the growth rate in cattle stocks has similar cycles to the series on the stock levels.