The maximum likelihood estimation is discussed for the NLAR model with Laplacian marginals. Since the explicit form of the estimates cannot be obtained due to the complicated nature of the likelihood function we utilize the automatic computer optimization subroutine using a direct search complex algorithm. The conditional least square estimates are used as initial estimates in maximum likelihood procedures. The results of a simulation study for the maximum likelihood estimates of the NLAR(1) and the NLAR(2) models are presented.