This paper examines the convexity bias, caused by the non-linearity of payoffs, in the pricing of interest rate swaps off the Eurocurrency futures curve. The evidence from four major currencies – $, £, DM and ¥ – during 1987–1996 suggests that swaps were initially being priced off the futures curve (ignoring the convexity adjustment); subsequently, the market swap rates drifted below the rates implied by futures prices. After rejecting alternative explanations, we use alternative term structure models to show that the convexity bias is related to the empirically observed swap-futures differential. We interpret these results as evidence of mispricing of swap contracts during the early years, which was eliminated over time.