Abstract This note deals with a special problem of estimating a contingency table arising in demographic analysis. What we require are the estimates of the numbers of births and deaths in Malaya crossclassified by state and race for the years of the Japanese occcupation, 1942-45. For many reasons this period had an adverse effect on the Chinese and Indian Communities, and hence the two-fold result of a greater reduction in the number of births and a larger increase in the number of deaths in states with a smaller proportion of Malay population. The estimates are worked out by means of a technique which takes into consideration this actual demographic situation.