Separable　nonlinear　models　frequently　arise　in　system　identification,　signal　analysis,　electrical　engineering,　and　machine　learning.　Their　parameter　optimization　belongs　to　a　class　of　separable　nonlinear　least　squares　(SNLLS)　problem.　Applying　the　classical　variable　projection　algorithm　to　the　SNLLS　problems　may　give　poor　generalization.　In　order　to　handle　complexity　control　and　ill-conditioned　nonlinear　least　squares　problems,　we　consider　in　this　paper　two　L2　regularization　algorithms　for　the　SNLLS　problems.　The　first　approach　is　to　directly　add　a　Tikhonov　penalty　to　the　objective　function　of　the　SNLLS　problem.　The　second　approach　is　to　replace　the　ordinary　linear　least　squares　problem　in　the　SNLLS　problem　by　a　Tikhonov　one.　We　give　their　difference　from　the　perspective　of　Bayesian.　Numerical　experiments　are　also　presented　to　compare　the　performance　of　the　two　regularized　algorithms.　Results　show　that　the　first　regularization　method　is　more　robust　than　the　second　one.　©　2019,　Springer　Nature　B.V.