The structural relaxation process has been examined by a Monte Carlo simulation for a two‐dimensional XY clock model that has two transition points, a Kosterlitz‐Thouless transition atTKTand a long range order transtiion atTC(TC<TKT). The system was quenched from the middle temperature phase betweenTCandTKTto low temperature phase belowTC. The structure relaxation rate at low temperature phase is slower for the initial middle temperature state that has been created directly from the high temperature phase aboveTKTthan that created from the low temperature phase belowTC, both middle temperature phases being kept for the time insufficient for equilibration.