This paper investigates the stationary characteristics of computed real interest rates with nominal interest rates and inflation for 22 OECD countries. Using quarterly data over the 2000 – 2010 period, LM unit root test is employed which endogenously determines up to two structural breaks in level and trend. The empirical findings suggest a combination of stationary and nonstationary results for real interest rates, nominal interest rates and inflation. Besides, the internal stationarity or nonstationary interactions of real and nominal interest rates are investigated by inflation. The results indicate that stationary nominal interest rates and inflation cause stationary real interest rates. At the same time nonstationary nominal interest rates and inflation could cause a stationary or nonstationary real interest rate with respect to cointegration. Stationary nominal interest rate and nonstationary real interest rate cause to nonstationary real interest rate while nonstationary nominal interest rate and stationary inflation could cause stationary or nonstationary real interest rate.