In the stability analysis of numerical methods for ordinary differential equations, the classical test equation
has been supplemented in the last fifteen years by essentially more complex, nonlinear problems. In a similar vein, the author suggests nonlinear model problems that can supplement the equation
in the study of the stability of methods for delay differential equations. While the backward Euler methods is found to perform well when applied to the new tests, this is not so for the (A-stable) Gauss collocation methods.