The results of the first investigations of the process of local decomposition of lead-lanthanum zirconate-titanate solid solution in the vicinity of the interphase boundaries separating domains of coexisting ferroelectric and antiferroelectric phases are presented. The solid solution with the composition: 6 at% of La, 73 at% of Zr, and 27 at% of Ti is considered. The kinetics of the local decomposition of this solid solution in the process of aging of samples quenched down to room temperature from the paraelectric phase is studied. The mechanisms that define the kinetics of the process of establishment of the equilibrium state of coexisting domains of ferroelectric and antiferroelectric phases are discussed.