This paper presents some recent time series models (the so-called NAREX(l) models) for exponential variables with first order autoregressive structures. They are analogs of the standard AR(1) model and of the EAR(l), NEAR(l), TEAR(l) and AREX(l) models, introduced by Lawrance, Lewis, Gaver, Malisic and others. Some of their models can be obtained from NAREX models as special cases. The distribution of the innovation sequences (a probability mixture) and the autoregressive structure of NAREX processes are discussed as well.