Abstract: In this thesis, the propagation of nonlinear ion-acoustic shock waves theoretically in magnetoplasma composed of cold viscous ions with two superthermal electrons is discussed. The reductive perturbation technique has been used to obtain the nonlinear Zakharov-Kuznetsov- Burgers equation to examine effective features of nonlinear ion-acoustic shock waves. The tanh method has applied to derive the analytical solutions of the nonlinear Zakharov-Kuznetsov- Burgers equation. Furthermore, the formation conditions of oscillatory and monotonic nonlinear shock wavesg structures have been discussed. The findings here demonstrate that the nonlinear ion-acoustic shock waves structures strongly depend on the superthermalities of cold and hot electrons, the ion kinematic viscosity, the concentration of cold superthermal electrons, the temperature ratio, the ion cyclotron frequency, and the direction cosines of the wave vector. Moreover, the present research may be useful for better understanding of the features of the nonlinear shock wave in astrophysical situations and space environment such as Saturn's magnetosphere.