The research was carried out in the Department of Research and Studies of the Department of Horticulture - Ministry of Agriculture in Abu Ghraib. The genetic diversity of six locally derived pure strains of the summer squash 1001, 1003, 1004, 1005, 1009 and 1010, the two genetically diversity strains were identified 1001and 1009 there doer used as parents (Testers) for three-way hybrids. Four inbred 1003, 1004, 1005, and 1010 in half diallel cross to get six single hybrids 1003*1004, 1003*1005, 1003*1010, 1004*1005, 1004*1010, 1005*1010, for use by mothers (lines) for the production of three-way hybrids, Triple hybrids produced according to the program of subtraction. (Line*tester) To estimate the hetrosis and the combining ability and some of the genetic parameters in the three-way hybrids for their studied traits.
The results showed that the best triple hybrid ((1004*1005) *1001) in plant yield, weight fruit, number of branches, weight of dry plant, number of female flowers, and ration bloody flowers. Which gave 5.08 Kg plant-1, 42.66 fruit plant-1, 4.17 branch plant-1, 71.30%, 30.65 female flower plant-1 and 27.95 bloody flower plant-1, On gave the hybrid vigor as compared to best parent 52.64%. The first parent 1001, showed highly general combining plant yield, weight fruit, number female flowers per plant, number of bloody flowers, While showing parent 1009, showed highly general combining weight fruit, fruit set percent, plant height, Wile brood sense heritability was high in all characteristics. In addition, narrow sense heritability was low in several traits important of which plant yield and weight fruite, the relation method of breeding to improve these traits is hybridization.