The main objective of this investigation was to estimate heterosis, genetic parameters, genetic advance under selection, heritability in broad and narrow sense for yield, its components, earliness, and fiber properties in an Egyptian cotton cross of Giza 80 x Giza 86. The results of the estimates of the parameters of gene effects indicated that additive, dominance and epistatic gene effects were involved in the inheritance of most traits, The non-additive components were greater in magnitude than additive component for most traits. Mid-parent heterosis was observed for all traits except for boll weight, while useful heterosis were detected only for seed cotton yield, days to first flower and micronaire value. Inbreeding depression was recorded only for seed cotton yield. Over-dominance appeared to control yield, boll numbers, days to first flower, fiber length, fiber strength and micronaire value. High or moderate broad sense heritability values were detected for all traits, while moderate narrow sense heritability was accounted only for lint percentage, days to first flower and all fiber properties. The phenotypic and genotypic correlation between seed cotton yield and each of lint yield, boll number, boll weight and seed index were positive and large in magnitude. Moreover, positive and significant genotypic correlations for seed cotton yield, lint yield and boll number with micronaire value and reflectance traits were detected. While negative genotypic correlation coefficient for the above mentioned yield traits were observed for days to first flower indicating that the increase in yield may improve earliness. Also, significant negative correlations were found between yield and both of fiber length, fiber strength and yellowness. Such undesirable associations need to be broken by suitable breeding techniques like recurrent selection or ^by billorental mating system to obtain newer and useful genetic recombinations for these characters.