We propose a generalization of the popular nonlinear ARX model structure by treating its parameters as varying over time. The parameters are considered generated by linear filters operating on the models regressors. The filters are expressed as a sum of atoms that are either sum of damped exponentials and sinusoids, or sinusoids with time varying frequencies. This form allows us to enforce stability of the parameter evolution as well as leverage the atomic norm minimization framework for inducing sparsity. It also facilitates easy incorporation of smoothness related priors that that making it possible to treat these models as nonlinear extensions of the familiar LPV models. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.