Ordinary differential equations, approximation for a class of neutral differential difference equations of the problem, the current popular studies have focused on a class of neutral differential difference equations in addition of constant results under the condition of less than zero, zero solution asymptotic stability of ordinary differential equations can be shown in close to a class of neutral differential difference equations, delay is sufficient and necessary conditions. However, the necessary and sufficient conditions of hysteresis are ignored under the condition that the sum of constants is equal to 0 (i.e. under the first critical condition).So the ordinary differential equations with approximation method, a class of neutral differential difference equations from constant within a class of neutral differential difference equations together, the result is less than 0 and is equal to zero, under the condition of two kinds of ordinary differential equations, respectively study the stability of zero solutions of can approach is shown in a class of neutral differential difference equations of delay sufficient and necessary conditions.