A criterion is given which is sufficient for the characteristic roots to remain within the semi-plane Rc (λ)<0. It is not necessary to find the roots of transcendental equation but, the traditional Gorshgorin criterion for each t≥t0, together with another condition are sufficient to determine the stability of tho IJ.G.M. systems. Dopplor effects due to variable time delays in Sandborg's non-linear model is being considered.