This paper analyses the implicit dynamics underlying the interest rate structure in Kenya. For this purpose, we use data on four interest rates of commercial banks (deposits, savings, lending and overdraft) together with the 91-day Treasury Bill rate, for the period July 1991 to August 2010, and apply various techniques based on long-range dependence and, in particular, on fractional integration. The results indicate that all series examined are nonstationary with orders of integration equal to or higher than 1 when using parametric techniques and slightly smaller than 1 when using semiparametric methods. The analysis of various spreads suggests that lending¿savings and deposits¿savings are also nonstationary I(1) variables; however, the spreads vis-à-vis the Treasury Bill rate may be mean reverting if the errors are autocorrelated. The high level of dependence observed in some of these series could be the result of an incorrect interest rate policy, implying the desirability of a policy aimed at reducing interest rate volatility.