The commercial future of Linum usitatissimum is intrinsically linked to its cultivation as a dual-purpose crop for producing increased seed and fibre yields. The present study evaluates 36 F 1 crosses derived from nine linseed/flax accessions for their potential as dual-purpose cultivars and/or their suitability for extracting new recombinants producing high seed yield as well as increased fibre output. The quantitative analysis indicated that variation between the F 1 families is largely but not exclusively due to the additive and non-additive (dominance) effects of genes. Dominance is high for plant height (H1), height at maturity (HMT), number of branches (NBr) and seed weight (SdWt) while 100 seed weight (Wt100) displays no dominance at all. The repeatability estimates representing the heritability of each trait, vary from low (0·20) for number of branches (NBr) to high (0·71) for height at flowering time (HFT). The dual-purpose traits such as seed weight (SdWt) and straw weight (StWt) were only moderately inherited while flowering time (FT) and various heights were rather highly heritable. A moderate and positive correlation ( r =0·57) between StWt and SdWt, and a completely independent inheritance of Wt100 suggested that there are good chances of combining these traits into a single genotype. The phenotypic performance of the crosses also confirmed this trend and at least four crosses showed superior performance for both SdWt and StWt compared to their parental lines. All these crosses involved a linseed line (B3) as a common parent and the second parent was either another linseed line (A1 and A3) or a flax accession (K3 and L2); none of the flax×flax crosses showed good potential for seed yield. While all four crosses possess the potential to become highly productive, dual-purpose, hybrid varieties, the extraction of desirable inbred lines from them, however, may prove difficult because the superior performance of the hybrids seems largely due to strong unidirectional dominance and high SCA effects.