In this paper we model real interest rates as a generalised mean rever
ting Ornstein Uhlenbeck process. Empirical tests of the model using US
and UK data for the period 1870-1975 shows that there exists signific
ant mean reversion in both the US and UK for real interest rates, infl
ation rates and nominal interest rates. We present evidence for some s
tylised empirical facts which might be incorporated in models linking
real interest rates, inflation and nominal interest rates.