In　this　paper,　we　consider　the　term　selection　problem　for　a　class　of　separable　nonlinear　models.　The　strategy　is　a　two-step　process　in　which　the　nonlinear　parameters　of　the　model　are　first　optimized　by　a　variable　projection　method,　and　then　the　least　absolute　shrinkage　and　selection　operator　are　adopted　to　obtain　a　sparse　solution　by　picking　out　the　critical　terms　automatically.　This　process　may　be　repeated　several　times.　The　proposed　algorithm　is　tested　on　parameter　estimation　problems　for　an　exponential　model　and　a　neural　network-based　model.　The　numerical　results　show　that　the　proposed　algorithm　can　pick　out　the　appropriate　terms　from　the　overparameterized　model　and　the　obtained　parsimonious　model　performs　better　than　other　methods.