The　generalized　exponential　autoregressive　(GExpAR)　models　are　extensions　of　the　classic　exponential　autoregressive　(ExpAR)　model　with　much　more　flexibility.　In　this　paper,　we　first　review　some　development　of　the　ExpAR　models,　and　then　discuss　the　stationary　conditions　of　the　GExpAR　model.　A　new　estimation　algorithm　based　on　the　variable　projection　method　is　proposed　for　the　GExpAR　models.　Finally,　the　models　are　applied　to　two　real　world　time　series　modeling　and　prediction.　Comparison　results　show　that　(i)　the　proposed　estimation　approach　is　much　more　efficient　than　the　classic　method,　(ii)　the　GExpAR　models　are　more　powerful　in　modeling　the　nonlinear　time　series.　(C)　2018　Elsevier　Inc.　All　rights　reserved.