The analysis ofk×kupper triangular contingency tables in which both margins have the same polytomy is considered. Such a table will arise whenksubjects form pairs (dyads) in which the pair (i,j)cannot be distinguished from (j,i), and individuals cannot form dyads with themselves. A quasi-independence model for such data is developed and extended to account for additional multiplicative factors. The resulting estimation procedures and goodness-of-fit tests are illustrated in two examples.