Estimates of Components of Variances for Bunch Traits in Date Palm Crosses (Phoenix dactylifera L )

2 f/m), while Non-significant negative additive variances ( σ 2 A) were obtained for all the traits. Dominance variance ( σ 2 D) showed significant positive values for number of fruits, spikelets, aborted fruits and unfertilized florets. Positive estimates were recorded for environmental variance ( σ 2 e), genotypic variance ( σ 2 g) and phenotypic variance ( σ 2 ph). In allcases phenotypic variance was much larger than the genotypic variance. Low environmental variance were obtained for the traits indicating that the environmental condition where the experiment was carried out is homogenous and the material could perform considerably well under similar environmental conditions. The means performance of the males indicates that variability exists between the males; Males 6R3 and 1R7 are good combiners with female 12R3 for number of fruits while males 1R12 and 5R2 are good combiners with female 12R3 for number of fruits. Female 2R8 is poor general combiners for number of fruits. Males 1R12 and 5R2 are good combiners with female 1R27 for weight of fruit while male 6R3 and 1R7 are good combiners with female 12R3 for fruit weight. Recurrent and backcross selection are recommended for further date palm improvement programs. Keywords: Male variances ( σ 2 m), female within male variances ( σ 2 f/m ), additive variances ( σ 2 A), Dominance variance ( σ 2 D), environment variance ( σ 2 e), phenotypic variance ( σ 2 ph ), genotypic variance( σ 2 g) and bunch traits .