Heath, Jarrow, and Morton (1992) present a general framework for modeling the term structure of interest rates which nests most other models as special cases. In their framework, the dynamics of the term structure and the prices of derivative instruments depend only upon the initial term structure and the forward rate volatility functions. Despite their importance, there has been little empirical work studying the forward rate volatility functions. This paper begins to fill this gap by estimating some nonparametric models of the forward rate volatilities. In a univariate model, the form of the forward rate volatility function differs for different maturities, and for some maturities appears not to be a monotonic function of the level of the forward rate. In a bivariate model, a measure of the "slope" of the term structure seems to have an important impact on the volatility. These results differ from the simple models that have been proposed and used in the literature.