This paper analyses the implicit dynamics underlying the interest rate structure in Kenya. For this purpose we use data on four commercial banks’ interest rates (Deposits, Savings, Lending and Overdraft) together with the 91-Day Treasury Bill rate, for the time period July 1991 – August 2010, and apply various techniques based on long-range dependence. The results indicate that all series examined are nonstationary with orders of integration equal to or higher than 1. The analysis of various spreads suggests that they also are nonstationary I(1) variables, the only evidence of mean reversion being obtained in the case of the Lending – Saving spread with autocorrelated errors