In　this　article,　we　study　the　recursive　algorithms　for　a　class　of　separable　nonlinear　models　(SNLMs)　in　which　the　parameters　can　be　partitioned　into　a　linear　part　and　a　nonlinear　part.　Such　models　are　very　common　in　machine　learning,　system　identification,　and　signal　processing.　Utilizing　the　special　structure　of　the　SNLMs,　we　propose　a　recursive　variable　projection　(RVP)　algorithm,　in　which　at　each　recursion,　the　linear　parameters　of　the　model　are　eliminated,　and　the　nonlinear　parameters　are　updated　by　the　recursive　Levenberg-Marquart　algorithm.　Then,　based　on　the　updated　nonlinear　parameters,　the　linear　parameters　are　updated　by　the　recursive　least-squares　algorithm.　According　to　a　convergence　analysis　of　the　RVP　algorithm,　the　parameter　estimation　error　is　mean-square　bounded.　Numerical　examples　confirm　the　satisfactory　performance　of　the　proposed　algorithm.