This study analyzes price and volatility transmissions between nineteen real estate investment trusts (REITs) and the oil markets. The REITs data represents a variety of countries at different stages of their development and the expanded analytical approach includes accounting for structural shifts as gradual processes - as opposed to strictly abrupt processes typically assumed in the literature. Oil prices are found to primarily predict REITs prices in mature REITs markets, but the feedback from REITs to oil prices is weak. From the perspective of volatility, strong evidence of bidirectional transmission in majority of the markets is observed. Our results are in general robust to a shorter common sample period of the various countries. This study further demonstrates the importance of accounting for gradual (smooth) structural shifts for price transmission analysis. (C) 2020 Elsevier B.V. All rights reserved.