Dynamic processes of the modelocked laser based on a auxiliary coupled cavity containing a nonlinear frequency-doubling crystal has been systematically studied in this paper. And, the specific formulas of the output pulse width of this modelocked laser in instantaneously dynamic equilibrium are given. Moreover, the results of nu-merical analysis and calculation show that its modelocking output properties are su-perior to that of the laser modelocked by an intracavity frequency-doubling crystal.