A family of sets is called a weak Delta-system if the cardinality of the in
tersection of any two sets is the same. We elaborate a construction by Rodl
and Thoma [9] and show that for large n, there exists a family F of subset
s of {1,..., n} without weak Delta-systems of siae 3 with \F\greater than o
r equal to 2(c(n log n)1/3).