The activity coefficient of component i is found by differentiation of the excess Gibbs energy towards x. 
This yields, when applied only to the first term and using the Gibbs–Duhem equation,:
In here A and A are constants which are equal to the logarithm of the limiting activity coefficients:  and  respectively.
When , which implies molecules of same molecular size but different polarity, the equations reduce to the one-parameter Margules activity model:
In that case the activity coefficients cross at x=0.5 and the limiting activity coefficients are equal.  When A=0 the model reduces to the ideal solution, i.e. the activity of a compound is equal to its concentration (mole fraction).