Data from the F1, F2 and F3 generations derived from four F1 hybrids of sunflower were analysed to determine the genetical control of eleven agronomically important traits namely, flowering time (FT), final height (FH), seed set (SS), fresh seed weight (FSW), dry seed weight (DSW), 25-seed weight (SSW), head diameter (HD), head angle (HA), neck width (NW), Botrylis infection (BI) and percentage oil content (PO), with the objective of assessing their potential for producing superior recombinant lines. Comparisons of means revealed significant differences between the F: generations of crosses for all the characters except FT. Model fitting indicated that these differences were attributed either to variation in the magnitude of the dominance component [h], or the projected mean of the Finfin; generation, m. Further, all the variation in the generation means was accounted for by the m and [h] parameters and epistasis was shown to be non-existent for almost all the traits. Analysis of the second degree statistics revealed the presence of additive genetic effects and most of the characters showed moderate heritability except for HD, which was highly heritable. All the crosses were predicted to produce significant numbers of transgressive segregants and consequently were expected to yield superior inbred lines and second cycle hybrids either to be released as varieties as such or to be utilized in future breeding work. The overall differences between the crosses, however, were not highly pronounced and therefore it was not possible to identify a cross which would yield markedly superior recombinant lines and F1 crosses compared to the others.