This study first uses the non-linear co-integration with structural breaks by Gregory and Hansen (1996) to examine whether non-linear co-integration exists between real estate investment trusts (REITs) and corresponding stock markets in the United States and Australia. Second, we employ the smooth transition vector-error correction model (STVECM) including the generalized autoregressive conditional heteroskedasticity (GARCH) model to separately explore the adjustment efficiencies of non-linear short-run REIT and corresponding stock return dynamics, as well as respective REIT return dynamics when the long-run disequilibrium occurs. The results show that a structural break co-integration exists between the equity and mortgage REITs and stock markets in the US, between the REITs and stock markets in the Australia and between the REIT markets in both the US and Australia. When there are large positive and negative deviations of STVECM, the adjustment speed of reverting to equilibrium of the S&P 500 index is greater than that of the Mortgage REIT index. However, when there are large positive (negative) deviations of STVECM, the adjustment speed of reverting to equilibrium of the Australian REIT (stock) index is greater, and that of the Australian REIT (US REIT) index is greater. In addition, by using a non-linear Granger causality test by Hiemstra and Jones (1994), we find that credit price effects exist between the US for each type of REIT and stock markets regardless of large positive or negative deviations (or returns) in STVECM (or STVAR). However, there is a feedback effect exists between the REITs and the stock markets in Australia.