The paper is devoted to the study of homothety’s influence on the number of optimal design support points under fixed values of regression model’s parameters. Two-dimension nonlinear by parameters Ayen—Peters model used in analytical chemistry is considered. It is shown that the number of optimal design support points has to be more or equal to the number of parameters depending on certain conditions. The optimal designs with the minimum number of support points are constructed explicitly. Some numerical methods for construction designs with bigger number (such designs are suggested to call excess designs) are used. Refs 16. Figs 2. Tables 2.