This paper examines time series properties of the swap spreads in three segments of the US dollar interest rate swaps market. Specifically, the relationship between the swap spreads in US dollar fixed-for-floating Interest Rate Swaps (IRS), Treasury bill versus LIBOR basis swaps and commercial paper versus LIBOR basis swaps are analysed. Tests for evidence of volatility spillover among these segments are conducted. Variations of several models, including VAR/VECM, GARCH (1, 1) EGARCH and GJR-GARCH are used in this study. Evidence of interdependencies and volatility spillover is found between these markets. Using the GJR-GARCH model, it is found that the spillover is asymmetric.