The European beech (Fagus sylvatica L.) is the most prevalent deciduous tree species in Central Europe. The implementation of sustainable, close-to-nature silvicultural practices increased the percentage share of beech in forest species composition, raising the economic significance of beech roundwood, especially in terms of revenues from timber sales. The elucidation of roundwood price mechanisms as well as long-term equilibrium relations between international markets may be helpful in calculating the profitability of beech roundwood production. The study material consists of quarterly time series of beech roundwood prices from Austria, Czechia, Germany, Poland, Slovakia, and Slovenia in the years 2005–2018. The price time series were described with a multiplicative model incorporating seasonal, cyclical, and irregular, as well as long-term trend components. The time series were decomposed using the Census X11 method. Stationarity was tested by means of the augmented Dickey–Fuller test (ADF) and the Kwiatkowski–Phillips–Schmidt–Shin test (KPSS). Cointegration was assessed using the Johansen and Engle–Granger methods. From 2005–2018, the highest mean beech roundwood prices were found for Austria (77.5 € m−3) and Germany, and the lowest for Poland and Slovakia. Roundwood prices were badly affected by the 2008/2009 financial crisis, which caused an approx. 27% decline. The prices of large-diameter beech logs exhibited seasonal fluctuations, typically reaching a maximum in Q1 and a minimum in Q3. The amplitude of those fluctuations was the highest in Slovenia in 2005 (10.1%), while in Czechia and Germany, seasonal effects increased over the period of study. The lowest seasonality was found in Slovakia and Austria (in the latter country it was not statistically significant). On an annual scale, cyclical changes generally accounted for the largest proportion of price variation, and were particularly pronounced in Poland (78.9%), Slovakia (78.6%), and Austria (69.2%). On the other hand, seasonal effects were predominant in the Slovenian (40.6%), German (34.1%), and Czech (33.3%) markets. In countries with price series of type I(0), simple correlation between stationary beech roundwood prices is positive and the strongest between Czechia–Poland and Czechia–Austria; on the other hand they are the weakest in the German market. In Slovakia and Slovenia with nonstationary price series, both Johansen’s and Engle-Granger’s cointegration tests indicated the absence of a long-term equilibrium between the analyzed beech timber markets. Results revealed integration between the prices of large-diameter beech logs in Czechia, Austria, and Poland. It should be mentioned that in this study, the time series of price used are rather short for long time cointegration analysis, which might prevent the proper detection of cointegration between all analyzed countries.