  We study the continuity equation of the Gauduchon metrics and establish its
interval of maximal existence, which extends the continuity equation of the
K\"ahler metrics introduced by La Nave \& Tian for and of the Hermitian metrics
introduced by Sherman \& Weinkove. Our method is based on the solution to the
Gauduchon conjecture by Sz\'ekelyhidi, Tosatti \& Weinkove.
