The stability analysis on a class of oscillatory systems whose controlled object has a standard form of second-order systems is presented. The effect of the signal transmission delay on the performance of the closed loop control system with unit negative feedback is discussed. The relationship between the time-delay and the stability of closed loop control system is obtained via drawing and analyzing the Nyquist plots in the different regions of the relative damping coefficient. The simulation example of unit step response for each case is processed and the simulation results show that the analysis is correct.