This　article　concentrates　on　the　recursive　identification　algorithms　for　the　exponential　autoregressive　model　with　moving　average　noise.　Using　the　decomposition　technique,　we　transform　the　original　identification　model　into　a　linear　and　nonlinear　subidentification　model　and　derive　a　two-stage　least　squares　(LS)　extended　stochastic　gradient　(ESG)　algorithm.　In　order　to　improve　the　parameter　estimation　accuracy,　we　employ　the　multi-innovation　identification　theory　and　develop　a　two-stage　LS　multi-innovation　ESG　algorithm.　A　simulation　example　is　provided　to　test　the　effectiveness　of　the　proposed　algorithms.　©　2020　John　Wiley　&　Sons　Ltd