The success of Linum usitatissimum as a commercial crop depends on its value for seed/oil (linseed) and/or fibre/straw production (flax). In the present study we evaluated nine linseed × linseed and two linseed × flax crosses for their potential to produce recombinant inbred lines (RILs) that give higher yields for dual-purpose (high seed–high fibre) traits. Analysis of the early generations indicated that while all crosses segregated for seed weight, straw weight, capsule weight and total plant weight, some crosses lacked the necessary genetic diversity to produce superior RILs. The performance of F3 families supported this conclusion as only two crosses were identified which had adequate potential to produce improved RILs with high seed and straw/fibre yields. The four most heterotic crosses identified in a previous experiment showed little potential for transgressive recombinants, although the best of these RILs would make better dual-purpose varieties compared to existing cultivars. Genotypic correlations were generally positive and should increase the chances of extracting RILs producing both high seed/oil and straw/fibre yields.