We present a discrete time, essentially affine, two Gaussian factors term structure model allowing for long memory. This feature allows to reconcile the strong persistence found in nominal yields and inflation with the theoretical properties of affine models, especially for long maturities. Model identification is achieved so that the factors have a clear economic interpretation. We find that extension of the model from short memory to long memory factors gives a substantial improvement in terms of fit of the model and forecast errors. Specifically, it seems crucial to model the expected inflation factor as a long memory process, while we don't find evidence of high persistence in the short rate dynamics. Based on the model estimates we compute the processes of real interest rates, real and nominal risk term premia, and inflation premia for different maturities. All these quantities are time varying. An accurate analysis of the insample as well as out-of-sample properties of the model is presented.