This study addressed two issues. First, it examined the ability of two models, developed by Cox, Ingersoll and Ross (CIR), to explain the differences between futures and implicit forward prices in the thirteen-week T-bill market. The models imply that if future interest rates are stochastic, futures and forward prices differ; the structural difference is due to the daily settlement process required in futures trading. Second, the study determined the efficiency of the thirteen-week T-bill futures market using volatility and regression tests. Volatility tests use variance bounds to examine whether futures prices are excessively volatile for the market to be efficient. Regression tests investigate whether futures prices are unbiased predictors of future spot prices. The study was limited to analysis of the first three futures contracts, using weekly price data as reported in the Wall Street Journal from March, 1976 to December, 1984. Testing of the first CIR model involved determination of whether changes in futures-forward price differences are related to changes in local covariances between T-bill futures and bond prices. The same procedure applied in testing the second model with respect to changes in futures-forward price differences, local covariances between T-bill spot and bond prices, and local variances of bond prices. Volatility tests of market efficiency involved comparison of mean variances on both sides of two inequality equations. Regression tests involved determination of whether slope coefficients are significantly different from zero.