This paper estimates real term structures from cross-sections of British government index-linked (‘realrd) bond prices. The Cox, Ingersoll, and Ross (1985) model is then fitted to the same data; the model closely approximates the shapes of the directly-estimated term structures. In contrast to similar studies of the nominal term structure, the long-term zero-coupon yield is quite stable, as the CIR model predicts, and in common with previous studies, the level of implied short rate volatility corresponds well with time series estimates. The other parameters, however, are often highly correlated and intertemporal parameter stability is rejected.