A numerical method has been proposed for solving strongly nonlinear si
multaneous equations with two variables by improving the Wegstein meth
od for one variable. The features of the proposed method are i) to use
only an initial value, ii) to provide stability of the solution with
simplicity of algorithm, and iii) to reduce the C. P. U. time required
. The superiority of this method is demonstrated by two sample calcula
tions, bubble point at chemical equilibrium and a quenching.