The identification of real estate cycles has always been an important issue in the study of real estate. This paper selected as indicators the Composite Leading Index and Reference Cycle Index regarding the real estate cycles in Taiwan, as they incorporate real estate activities, such as investments, production, transactions and utilization. This paper applied the bivariate Markov-switching autoregressive model (MS-ARX) and the Markov-switching vector auto-regression model (MSVAR) to identify the turning points of real estate cycles. The empirical results indicate that both intercepts and variances were subject to the influence of unobservable variables. Also, the models with the best fit are MSIAH (2)-VAR (8) with the lags being 8 and L (1) – MSIH (2)-AR (8) with the lags being 8 and the intercepts, coefficients and co-variances are subject to the influence of state variables. Both models showed that the real estate cycles in Taiwan are undergoing contraction rather than expansion. This is in line with the results published by Taiwan Real Estate Research Center. Generally speaking, L(1)-MSIH(2)-ARX(8) and MSIAH(2)-VAR(8) produced rather accurate results in terms of identifying the turning points of real estate cycles in Taiwan.