The parameter of a nonlinear regression model is determined uniquely for al¬most all experimental designs if the number of experimental points is greater than the dimension of the parameter and different regression functions have no weak contact of infi¬nite order. This result yields global identifiability for most practically used curve-fitting models, especially with polynomial, exponential and trigonometric regression functions. In this approach regression models with errors of measurement in the independent variables are included as well.