This is a report on a study of racial interrelationships among students in desegregated schools. Sociometric measures of third graders' willingness to play and work with their classmates (indicating cross-race acceptance) showed evidence of racial bias; however, the amount of bias appeared small compared to the findings of earlier studies which used measures of friendship rather than acceptance as indicators of interracial relationships. Significantly, children tended to demonstrate sex bias more than racial bias in interpersonal relationships. Observation of children's classroom interactions corroborated these findings. Follow-up studies of the same group of third graders when they were in the sixth grade and in the tenth grade indicated increasing own-race preference and decreasing own-sex preference over time; comparisons of acceptance and friendship measures suggested similar changes in race and sex preferences with advancing grade levels. Among the reasons given for increasing own-race preference with increases in age were school organizational features which might influence the degree of interracial contact, and the personal identities that each group projects and interprets. It was emphasized that the findings of more positive cross-race relations when the criterion is acceptance rather than friendship provide cause for optimism about integrated education. (Author/MJL)