In this paper the mode coupling equations are used to study double-frequeney dye laser with a compound cavity. The double-frequency stable operation condition, the condition of inhibiting broad-band oscillations and the intensity ratio of two frequencies are deduced. Using a graphical method it has been found that this kind of laser has four typical tuning processes and some parameters can been conveniently obtained. Two new designs for double-frequency flashlamp-pumped dye laser with a compound cavity are discribed. The experimental results agree with, the theory on the whole.