Data from the NA31 experiment at CERN have been used for a search for
the decay mode K(L) --> pi0pi0gamma. After all cuts, three events rema
in in the signal region with an estimated background of 2.2 +/- 0.9 ev
ents. The upper limit for the branching ratio of K(L) --> pi0pi0gamma
is 5.6 X 10(-6) at the 90% confidence level.