New optimum design methods for dynamic vibration absorbers are proposed for the cases when the primary system has some uncertainty in its dynamic characteristics and the excitation frequency fluctuates in a small range. In the previous paper, we derived exact and very simple design equations that give the optimum natural frequency and damping ratio of the absorber for a given excitation frequency range in the special case that the excitation force amplitude is proportional to the square of the frequency and the objective function is the velocity amplitude. In this paper, an approximate design method of dynamic vibration absorbers for a general excitation force and a general objective function is discussed . Two different types of approximate design equation are proposed and calculation results obtained by using the proposed design methods are compared with the exact solution obtained by using a numerical method. Through the discussion, it is demonstrated that the proposed design methods are very useful.