In this paper, the stability of time-delayed DC motor speed control systems is analyzed. The measurement devices and communication links used by networked control systems, cause a significant amount of time delays. The stability boundary of the system in terms of the time delay is theoretically determined and an expression is obtained to compute the delay margin in terms of system parameters. The delay margin is defined as the maximum amount of time delay for which the DC motor speed control system is marginally stable. The results indicate that the system becomes unstable if the time delay exceeds the delay margin at a given set of parameters. Theoretical delay margin results are verified using the time-domain simulations of MATLAB/Simulink.