Abstract: Presents several necessary and sufficient conditions of the mean square ergodic with regard to the mean value and the correlation function for a multiple parameter widesense stationary process , viz . when the process is mean square continuous , a necessary and sufficient condition of the mean square ergodic with regard to the mean value is that the jump value F(0) - F(0 - )at the origin of the process' spectral function equals | m |2, where m is the mean value of the process; and if the process' mean value is zero and the process is mean square continuous, real valued and normal ,then a necessary and sufficient condition of the mess square ergodic with regard to the correlation function is that the process spectral function be continuous .