Affine models are very popular in modeling financial time series as they allow for analytical calculation of prices of financial derivatives like treasury bonds and options. The main property of affine models is that the conditional cumulant function, defined as the logarithmic of the conditional characteristic function, is affine in the state variable. Consequently, an affine model is Markovian, like an autoregressive process, which is an empirical limitation. The paper generalizes affine models by adding in the current conditional cumulant function the past conditional cumulant function. Hence, generalized affine models are non-Markovian, such as ARMA and GARCH processes, allowing one to disentangle the short term and long-run dynamics of the process. Importantly, the new model keeps the tractability of prices of financial derivatives. This paper studies the statistical properties of the new model, derives its conditional and unconditional moments, as well as the conditional cumulant function of future aggregated values of the state variable which is critical for pricing financial derivatives. It derives the analytical formulas of the term structure of interest rates and option prices. Different estimating methods are discussed (MLE, QML, GMM, and characteristic function based estimation methods). Three empirical applications developed in companion papers are presented. The first one based on Feunou (2007) presents a no-arbitrage VARMA term structure model with macroeconomic variables and shows the empirical importance of the inclusion of the MA component. The second application based on Feunou and Meddahi (2007a) models jointly the high-frequency realized variance and the daily asset return and provides the term structure of risk measures such as the Value-at-Risk, which highlights the powerful use of generalized affine models. The third application based on Feunou, Christoffersen, Jacobs and Meddahi (2007) uses the model developed in Feunou and Meddahi (2007a) to price options theoretically and empirically. (Joint with Bruno Feunou).