The analysis of k × k upper triangular contingency tables in which both margins have the same polytomy is considered. Such a table will arise when k subjects 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. © 1976, Taylor & Francis Group, LLC.