An experiment was carried out in the vegetables field of Horticulture Department / College of Agriculture / Baghdad University , for the three seasons : spring and Autumn of 2005 , and spring of 2007 , to study the type of gene action in some traits of vegetative , flowery growth , yield and its components in summer squash crosses (4 x 3 = cross 1 , 3 x 7 = cross 2 , 3 x 4 = cross 3 , 3 x 5 = cross 4 , 5 x 1= cross 5 , 5 x 2 = cross 6). The study followed generation mean analysis method which included to each cross (P1 , P2 , F1 , F2 , Bc1P1 , Bc1P2) , and those populations obtained by hybridization during the first and second seasons. Experimental comparison was performed in the second (Two crosses only) and third seasons , (four crosses) by using RCBD with three replications. Three parameters model with chi square test and six parameters model were used to estimate the type of gene effects , in breeding depression , components of genetic variance , mean degree of dominance , heritability and expected gain due to selection. The results showed that dominance and epistatic (additive x additive) and (dominance x dominance) effects were great importance than additive effects in most traits of all crosses. In breeding depression was important except for plant length . Broad sense heritability ranged from 51.68 – 90.25% for plant length in crosses 3 , 5 and 6 while narrow – sense heritability was high (76.6 and 83.9%) for No. of leaves in crosses , 2,5 respectively and (57.13%) for No. of Nodes to first female flower in cross 6. Expected gain due to selection among F2 was agreat (29.5%) for No. of leaves in cross 5 while it was low to moderate some traits in other crosses. Also the results showed in yield and its component that dominance and epistatic (additive x additive) and (dominance x dominance) effects were great importance than additive effects in most traits of all crosses. In breeding depression was important except for fruit weight . Broad sense heritability was high in fruit weight , plant yields , and total yield (67.05 , 52.54 , 52.56) respectively for cross 1 , while it was low to moderate in some traits and crosses and narrow – sense heritability was high in fruit weight (40.82) for cross 6 and low in some traits to some crosses. Expected gain due to selection was low in plant yield and total yield for cross 4 and fruit weight for cross 6.