Abstract: Using the method of characteristic lines this paper considers the global C¹ solution of the Cauchy problem for two-dimensional gas dynamics system. When the initial data degenerate to the special case ρ₀(x, y)=const, the global C¹ solution is obtained. For the case of isentropic exponent γ=1, a transformation about variables is introduced, which changes the system to a first order linear hyperbolic system with constant coefficients and the global C¹ solution is also obtained in this case when the initial data of the forms (ρ₀(x, y), u₀(x, y), v₀(x, y))=(exp(ω₀₁ (c₁x+d₁y)+ω₀₂(c₂x+d₂y)), u₀₁(c₁x+d₁y)+u₀₂(c₂x+d₂y), u₀₁(c₁x+d₁y)+u₀₂(c₂x+d₂y)), where c_i and d_i(i=1, 2) are constants.