Multivariable additive nonparametric regression model is a nonparametric regression model that involves more than one predictor and has additively separable function on each predictor. There are many functions that can be used on nonparametric regression models, such as the kernel, splines, wavelets, lokal polinomial and fourier series. This research focuses on multivariable additive nonparametric regression models as a result of between non trend fourier series. The estimation method that be used to obtain the estimators is Penalized Least Square. This method requires the estimation of smoothing parameters in the optimation process for obtaining the estimator of multivariable additive nonparametric regression model that  has been successfully obtained, which consists of an estimator of fourier series non-trend. The results of this theoretical study shows that the Penalized Least Square method works simultaneously for obtaining the estimators of the smoothing parameters and nonparametric regression models parameters as a result of non-trend fourier series which are additively separable.