Additive nonlinear systems are one of the most widely used nonlinear and non-parametric models to describe nonlinear behaviors. A number of analysis and identification techniques have been developed in the literature for such systems. To apply, however, one has to make sure that the system is additive or can be approximated well by an additive system. This is a nontrivial problem and has eluded researchers for a long time. To the best of our knowledge, only scatter results are reported in the literature. The difficulties lie in the fact that the function and its structure are unknown so estimating its derivatives under an unknown multidimensional density function could be subject to the curse of dimensionality. In this paper, we present two methods to check if a system is additive. The first one estimates the squared derivative average via the Fourier transform. The other one directly estimates the squared derivative average in a reproducing kernel Hilbert space (RKHS) setting. For both methods, convergence results are established and practical numerical algorithms are developed. (C) 2019 Elsevier Ltd. All rights reserved.