Abstract: Multiple functional regression models are a useful extension of classical multiple linear model. This paper focuses on the variable selection of multiple functional regression models with autoregressive errors. Based on Group SCAD (Smoothly Clipped Absolute Deviation) penalty, we study the variable selection of functional covariates and the order of the autoregressive error term simultaneously. In addition, we provide the selection consistency and asymptotic normality under mild conditions, and demonstrate its performance through simulation studies.