A　novel　parameter　identification　method　for　locally　linear　radial　basis　function-based　autoregressive　models　in　presence　of　colored　noises　is　proposed　in　this　paper.　Taking　advantage　of　the　global　nonlinear　and　local　linear　structural　characteristics　of　the　models,　two　dynamical　criterion　functions　are　constructed　based　on　the　separated　parameters　to　realize　the　dynamical　acquisition　and　utilization　of　the　entire　process　data.　Two　recursive　gradient　sub-algorithms　are　derived　for　estimating　the　separated　parameters　by　using　the　nonlinear　gradient　optimization.　To　coordinate　the　associated　variables　existing　in　the　sub-algorithms　and　to　estimate　the　unmeasurable　noise　terms,　we　combine　the　sub-algorithms　and　propose　a　two-stage　extended　recursive　gradient　(2S-ERG)　algorithm.　In　addition,　an　extended　recursive　gradient　algorithm　is　given　as　a　comparison.　The　feasibility　of　the　2S-ERG　algorithm　is　validated　by　numerical　simulations.(c)　2022　ISA.　Published　by　Elsevier　Ltd.　All　rights　reserved.