Previous studies often assume a linear relation between term premiums on Treasury securities and forward interest rates even though a nonlinear relation is a theoretical and an empirical possibility. To examine the relation, this paper uses a nonparametric kernel approach that permits both linear and nonlinear associations. The linear specification yields conditional expectations of term premiums that are similar to those predicted by the kernel approach only at the mean forward premiums. Generally, kernel estimation shows that the responses of expected term premiums to changes in forward premiums are time-varying and are significantly different from the constant slope coefficients produced by linear estimations. The evidence also shows that forward premiums contain much more information content for predicting future term premiums than has been found with linear estimation procedures.