Group Divisible Designs with Two Associate Classes:n=2 orm=2

In this paper we find necessary and sufficient conditions for the existence of a group divisible design GDD(n, m) of index (λ1, λ2) in whichn=2 orm=2, thereby completing the solution of the existence problem for alln,m,λ1, andλ2. In the process, necessary and sufficient conditions are found for the existence of anx-regular partial triple system whose complement inλKnhas a 1-factorization.