Multifrequency dynamical theory of pulsed CO2 lasers is extended. By substituting optical field equations for optical intensity equations, a theoretical model for injection locking of pulsed CO2 lasers is presented. The output power, instantaneous frequency and gain coefficient are calculated with the classic fourth order Runge-Kutta method for different input signal intensity and detuning frequency. The mode-locking stability of injection-locked broad tuned TEA CO2 lasers is studied. Calculated results show that for frequency detuning of 600 MHz, the injected intensity should be two orders of magnitude larger than that at frequency center for stable injection locking. Theoretical results agree well with the published experimental data. Further study indicates that, when gas pressure is up to 106 Pa, for the same tuning range, the injection intensity is only about 10% higher than the intensity at frequency center.